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Stochastic gene expression poses an important challenge for engineering robust behaviors in a heterogeneous cell population. Cells address this challenge by operating on distributions of cellular responses generated by noisy processes. Similarly, a previously published temporal logic gate considers the distribution of responses across a cell population under chemical inducer pulsing events. The design uses a system of two integrases to engineer an E. coli strain with four DNA states that records the temporal order of two chemical signal events. The heterogeneous cell population response was used to infer the timing and duration of the two chemical signals for a small set of events. Here we use the temporal logic gate system to address the problem of extracting information about chemical signal events. We use the heterogeneous cell population response to infer whether any event has occurred or not and also to infer its properties such as timing and amplitude. Bayesian inference provides a natural framework to answer our questions about chemical signal occurrence, timing, and amplitude. We develop a probabilistic model that incorporates uncertainty in the how well our model captures the cell population and in how well a sample of measured cells represents the entire population. Using our probabilistic model and cell population measurements taken every five minutes on generated data, we ask how likely it was to observe the data for parameter values that describe square-shaped inducer pulses. We compare the likelihood functions associated with the probabilistic models for the event with the chemical signal pulses turned on versus turned off. Hence, we can determine whether an event of chemical induction of integrase expression has occurred or not. Using Markov Chain Monte Carlo, we sample the posterior distribution of chemical pulse parameters to identify likely pulses that produce the data measurements. We implement this method and obtain accurate results for detecting chemical inducer pulse timing, length, and amplitude. We can detect and identify chemical inducer pulses as short as half an hour, as well as all pulse amplitudes that fall under biologically relevant conditions.  
The acrobot is a simple mechanical system patterned after a gymnast performing on a single parallel bar. By swinging her legs, a gymnast is able to bring herself into an inverted position with her center of mass above the part and is able to perform manuevers about this configuration. This report studies the use of nonlinear control techniques for designing a controller to operate in a neighborhood of the manifold of inverted equilibrium points. The techniques described here are of particular interest because the dynamic model of the acrobot violates many of the necessary conditions required to apply current methods in linear and nonlinear control theory. <p> The approach used in this report is to approximate the system in such a way that the behavior of the system about the manifold of equilibrium points is correctly captured. In particular, we construct an approximating system which agrees with the linearization of the original system on the equilibrium manifold and is full state linearizable. For this class of approximations, controllers can be constructed using recent techniques from differential geometric control theory. We show that application of control laws derived in this manner results in approximate trajectory tracking for the system under certain restrictions on the class of desired trajectories. Simulation results based on a simplified model of the acrobot are included.  +
We introduce an algorithm for the optimal control of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We compute directly on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. Each individual reachability problem is solved via the Hamilton-Jacobi-Bellman (HJB) partial differential equation of stochastic optimal control theory. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the partial differential equation allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to conservatively satisfy a complex temporal logic specification.  +
We introduce an algorithm for the optimal con- trol of stochastic nonlinear systems subject to temporal logic constraints on their behavior. We directly compute on the state space of the system, avoiding the expensive pre-computation of a discrete abstraction. An automaton that corresponds to the temporal logic specification guides the computation of a control policy that maximizes the probability that the system satisfies the specification. This reduces controller synthesis to solving a sequence of stochastic constrained reachability problems. The solution to each reachability problem corresponds to the solution to a corresponding Hamilton-Jacobi-Bellman (HJB) partial differential equation. To increase the efficiency of our approach, we exploit a class of systems where the HJB equation is linear due to structural assumptions on the noise. The linearity of the PDE allows us to pre-compute control policy primitives and then compose them, at essentially zero cost, to satisfy a complex temporal logic specification.  +
A computational approach to generating aggressive trajectories in real-time for constrained mechanical systems is presented. The algorithm is based on a combination of nonlinear control theory, spline theory, and sequential quadratic programming. It is demonstrated that real-time trajectory generation for constrained mechanical systems is possible by mapping the problem to one of finding trajectory curves in a lower dimensional space. Performance of the algorithm is compared with existing optimal trajectory generation techniques. Numerical results are reported using the NTG software package.  +
This paper presents an optimization framework for broadcast power-control, specifically addressed at wireless networking issues arising in implementing information flows for multi-vehicle systems. We formulate an optimization problem for the minimization of an aggregate cost subject to a constraint on a quantity we call the geometric connection robustness, which is a locally computable numerical assessment of the robustness of the an information flow to perturbations in position. Our main result is a location-aided distributed power-control algorithm based on a gradient-like optimization scheme. We also use geometric connection robustness to develop a cheap distributed heuristic for the construction of sparse connected information flow.  +
In an aircraft electric power system, one or more supervisory control units actuate a set of electromechanical switches to dynamically distribute power from generators to loads, while satisfying safety, reliability, and real-time performance requirements. To reduce expensive redesign steps, this control problem is generally addressed by minor incremental changes on top of consolidated solutions. A more systematic approach is hindered by a lack of rigorous design methodologies that allow estimating the impact of earlier design decisions on the final implementation. To achieve an optimal implementation that satisfies a set of requirements, we propose a platform-based methodology for electric power system design, which enables independent implementation of system topology (i.e., interconnection among elements) and control protocol by using a compositional approach. In our flow, design space exploration is carried out as a sequence of refinement steps from the initial specification toward a final implementation by mapping higher level behavioral and performance models into a set of either existing or virtual library components at the lower level of abstraction. Specifications are first expressed using the formalisms of linear temporal logic, signal temporal logic, and arithmetic constraints on Boolean variables. To reason about different requirements, we use specialized analysis and synthesis frameworks and formulate assume guarantee contracts at the articulation points in the design flow. We show the effectiveness of our approach on a proof-of-concept electric power system design.  +
Insects exhibit unparalleled and incredibly robust flight dynamics in the face of uncertainties. A fundamental principle contributing to this amazing behavior is rapid processing and convergence of visual sensory information to flight motor commands via spatial wide-field integration, accomplished by motion pattern sensitive interneurons in the lobula plate portion of the visual ganglia. Within a control-theoretic framework, a model for wide-field integration of retinal image flow is developed, establishing the connection between image flow kernels (retinal motion pattern sensitivities) and the feedback terms they represent. It is demonstrated that the proposed output feedback methodology is sufficient to give rise to experimentally observed navigational heuristics as the centering and forward speed regulation responses exhibited by honeybees.  +
A reactor for the deposition of superconducting \ybcolong\;thin films is modeled and studied from a control perspective to determine the heat transfer dynamics of the reactor under active thermal control. A nonlinear wavelength-dependent heat transfer model is developed to predict reactor heat transfer throughout the film growth process, and preliminary component testing is conducted to validate the model. The model is linearized about a typical operating point and analyzed with linear feedback control methods to determine the performance of the reactor under observer-based feedback control with film growth disturbances. The controller and observer are selected through linear quadratic regulator and linear quadratic estimator methods. Rates of convergence of the controller and observer are determined through examination of the eigenvalues of the linearized system, and disturbance rejection is assessed with ${\mathcal H}_2$ and ${\mathcal H}_\infty$ norms. The eigenvalue and norm analysis is applied to varying reactor design parameters to quantify performance tradeoffs. The maximum errors associated with control and with estimation of a nominal design case are both 21 K, and the longest time scales are 45 seconds and 10 seconds for the controller and observer, respectively.  +
This paper describes the use of a domain-specific language, and an accompanying software tool, in constructing correct- by-construction control protocols for aircraft electric power systems. Given a base topology, the language consists of a set of primitives for standard specifications. The accompanying tool converts these primitives into formal specifica- tions, which are used to synthesize control protocols. We can then use TuLiP, a Python-based software toolbox, to synthesize centralized and distributed controllers. For sys- tems with no time involved in the specifications, this tool also provides an option to output specifications into a SAT-solver compatible format, thus reducing the synthesis problem to a satisfiability problem. We provide the results of our synthesis procedure on a range of topologies.  +
This paper explores the problem of finding a real--time optimal tra jectory for unmanned air vehicles (UAV) in order to minimize their probability of detection by opponent multiple radar detection systems. The problem is handled using the Nonlinear Tra jectory Generation (NTG) method developed by Milam et al. The paper presents a formulation of the trajectory generation task as an optimal control problem, where temporal constraints allow periods of high observability interspersed with periods of low observability. This feature can be used strategically to aid in avoiding detection by an opponent radar. The guidance is provided in the form of sampled tabular data. It is then shown that the success of NTG on the proposed low--observable tra jectory generation problem depends upon an accurate parameterization of the guidance data. In particular, such an approximator is desired to have a compact architecture, a minimum number of design parameters, and a smooth continuously--differentiable input-output mapping. Artificial Neural Networks (ANNs) as universal approximators are known to possess these features, and thus are considered here as appropriate candidates for this task. Comparison of ANNs against B-spline approximators is provided, as well. Numerical simulations on multiple radar scenarios illustrate UAV trajectories optimized for both detectability and time.  +
In this paper we present a dynamical systems representation for multi-agent rendezvous on the phase plane. We restrict our attention to two agents, each with scalar dynamics. The problem of rendezvous is cast as a stabilization problem, with a set of constraints on the trajectories of the agents, defined on the phase plane. We also describe a method to generate control Lyapunov functions that when used in conjunction with a stabilizing control law, such as Sontag's formula, make sure that the two-agent system attains rendezvous. The main result of this paper is a Lyapunov-like certificate theorem that describes a set of constraints, which when satisfied are su±cient to guarantee rendezvous.  +
In this paper analysis of interconnected dynamical systems is considered. A framework for the analysis of the stability of interconnection is given. The results from Fax and Murray that studies the SISO-case for a constant interconnection matrix are genralized to the MIMO-case where arbitrary interconnection is allowed. The analysis show existness of a separation principle that is very useful in the sense of the simplicity for stability analysis. Stability could be checked graphically using a Nyquist-like criterion. The problem with time-delays and interconnection variation and robustness appear to be natural special cases of the general framework, and hence, simple stability criteria are derived easly.  +
In this paper, we analyze the problem of bifurcation control from a geometric perspective. Our goal is to provide coordinate free, geometric conditions under which control can be used to alter the bifurcation properties of a nonlinear control system. These insights are expected to be useful in understanding the role that magnitude and rate limits play in bifurcation control, as well as giving deeper understanding of the types of control inputs that are required to alter the nonlinear dynamics of bifurcating systems. We also use a model from active control of rotating stall in axial compression systems to illustrate the geometric sufficient conditions of stabilizability.  +
In the geometric theory of nonlinear control systems, the notion of a distribution and the dual notion of codistribution play a central role. Many results in nonlinear control theory require certain distributions to be integrable. Distributions (and codistributions) are not generically integrable and, moreover, the integrability property is not likely to persist under small perturbations of the system. Therefore, it is natural to consider the problem of approximating a given codistribution by an integrable codistribution, and to determine to what extent such an approximation may be used for obtaining approximate solutions to various problems in control theory. In this note, we concentrate on the purely mathematical problem of approximating a given codistribution by an integrable codistribution. We present an algorithm for approximating an m-dimensional nonintegrable codistribution by an integrable one using a homotopy approach. The method yields an approximating codistribution that agrees with the original codistribution on an m-dimensional submanifold E_0 of R^n.  +
We introduce a MATLAB-based simulation toolbox, called txtlsim, for an Escherichia coli-based Transcription–Translation (TX–TL) system. This toolbox accounts for several cell-free-related phenomena, such as resource loading, consumption and degradation, and in doing so, models the dynamics of TX–TL reactions for the entire duration of solution phase batch-mode experiments. We use a Bayesian parameter inference approach to characterize the reaction rate parameters associated with the core transcription, translation and mRNA degradation mechanics of the toolbox, allowing it to reproduce constitutive mRNA and protein-expression trajectories. We demonstrate the use of this characterized toolbox in a circuit behavior prediction case study for an incoherent feed-forward loop.  +
The T7 bacteriophage RNA polymerase (T7 RNAP) serves as a model for understanding RNA synthesis, as a tool for protein expression, and as an actuator for synthetic gene circuit design in bacterial cells and cell-free extract. T7 RNAP is an attractive tool for orthogonal protein expression in bacteria owing to its compact single subunit structure and orthogonal promoter specificity. Understanding the mechanisms underlying T7 RNAP regulation is important to the design of engineered T7-based transcription factors, which can be used in gene circuit design. To explore regulatory mechanisms for T7 RNAP-driven expression, we developed a rapid and cost-effective method to characterize engineered T7-based transcription factors using cell-free protein synthesis and an acoustic liquid handler. Using this method, we investigated the effects of the tetracycline operator’s proximity to the T7 promoter on the regulation of T7 RNAP-driven expression. Our results reveal a mechanism for regulation that functions by interfering with the transition of T7 RNAP from initiation to elongation and validates the use of the method described here to engineer future T7-based transcription factors.  +
This paper considers the problem of motion planning for a car-like robot (i.e., a mobile robot with a nonholonomic constraint whose turning radius is lower-bounded). We present a fast and exact planner for our mobile robot model, based upon recursive subdivision of a collision-free path generated by a lower-level geometric planner that ignores the motion constraints. The resultant trajectory is optimized to give a path that is of near-minimal length in its homotopy class. Our claims of high speed are supported by experimental results for implementations that assume a robot moving amid polygonal obstacles. The completeness and the complexity of the algorithm are proven using an appropriate metric in the configuration space R2 x S1 of the robot. This metric is defined by using the length of the shortest paths in the absence of obstacles as the distance between two configurations. We prove that the new induced topology and the classical one are the same. Although we concentration upon the car-like robot, the generalization of these techniques leads to new theoretical issues involving sub-Riemannian geometry and to practical results for nonholonomic motion planning.  +
We present an identification framework for biochemical systems that allows multiple candidate models to be compared. This framework is designed to select a model that fits the data while maintaining model simplicity. The model identification task is divided into a parameter estimation stage and a model comparison stage. Model selection is based on calculating Akaike's Information Criterion, which is a systematic method for determining the model that best represents a set of experimental data. Two case studies are presented: a simulated transcriptional control circuit and a system of oscillators that has been built and characterized in vitro. In both examples the multi-model framework is able to discriminate between model candidates to select the one that best describes the data.  +
A computationally e±cient technique for the numerical solution of constrained optimal control problems governed by one-dimensional partial differential equations is considered in this paper. This technique utilizes inversion to map the optimal control problem to a lower dimensional space. Results are presented using the Nonlinear Trajectory Generation software package (NTG) showing that real-time implementation may be possible.  +
In this paper we discuss a resilient, risk-aware software architecture for onboard, real-time autonomous operations that is intended to robustly handle uncertainty in space- craft behavior within hazardous and unconstrained environ- ments, without unnecessarily increasing complexity. This architecture, the Resilient Spacecraft Executive (RSE), serves three main functions: (1) adapting to component failures to allow graceful degradation, (2) accommodating environments, science observations, and spacecraft capabilities that are not fully known in advance, and (3) making risk-aware decisions without waiting for slow ground-based reactions. This RSE is made up of four main parts: deliberative, habitual, and reflexive layers, and a state estimator that interfaces with all three. We use a risk-aware goal-directed executive within the deliberative layer to perform risk-informed planning, to satisfy the mission goals (specified by mission control) within the specified priorities and constraints. Other state-of-the-art algorithms to be integrated into the RSE include correct-by-construction control synthesis and model-based estimation and diagnosis. We demonstrate the feasibility of the architecture in a simple implementation of the RSE for a simulated Mars rover scenario.  +
Safety guarantees are built into a robust MPC (Model Predictive Control) algorithm for uncertain nonlinear systems. The algorithm is designed to obey all state and control constraints and blend two operational modes: (I) standard mode guarantees resolvability and asymptotic convergence to the origin in a robust receding-horizon manner; (II) safety mode, if activated, guarantees containment within an invariant set about a safety reference for all time. This research is motivated by physical vehicle control-algorithm design (e.g. spacecraft and hovercraft) in which operation mode changes must be considered. Incorporating safety mode provides robustness to unexpected state-constraint changes; e.g., other vehicles crossing/stopping in the feasible path, or unexpected ground proximity in landing scenarios. The safety-mode control is provided by an offline designed control policy that can be activated at any arbitrary time during standard mode. The standard-mode control consists of separate feedforward and feedback components; feedforward comes from online solution of a FHC (Finite-Horizon optimal Control problem), while feedback is designed offline to generate an invariant tube about the feedforward tra jectory. The tube provides robustness (to uncertainties and disturbances in the dynamics) and guarantees FHC resolvability. The algorithm design is demonstrated for a class of systems with uncertain nonlinear terms that have norm-bounded Jacobians.  +
It has been shown that optimal controller synthesis for positive systems can be formulated as a linear program. Leveraging these results, we propose a scalable iterative algo- rithm for the systematic design of sparse, small gain feedback strategies that stabilize the evolutionary dynamics of a generic disease model. We achieve the desired feedback structure by augmenting the optimization problems with `1 and `2 regular- ization terms, and illustrate our method on an example inspired by an experimental study aimed at finding appropriate HIV neutralizing antibody therapy combinations in the presence of escape mutants.  +
This paper proposes a set-based parameter identi- fication method for biochemical systems. The developed method identifies not a single parameter but a set of parameters that all explains time-series experimental data, enabling the systematic characterization of the uncertainty of identified parameters. Our key idea is to use a state-space realization that has the same input-output behavior as experimental data instead of the experimental data itself for the identification. This allows us to relax the originally nonlinear identification problem to an LMI feasibility problem validating the norm bound of an error system. We show that regions of parameters can be efficiently classified into consistent and inconsistent parameter sets by combining the LMI feasibility problems and a generalized bisection algorithm.  +
We study the synthesis problem of an LQR controller when the matrix describing the control law is constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in a decentralized fashion; with the information flow being dictated by the constraints of a pre-specified topology. In this paper, we consider the finite-horizon version of the problem and provide both a computationally intensive optimal solution and a sub-optimal solution that is computationally more tractable. Then we apply the technique to the decentralized vehicle formation control problem and show that the loss in performance due to the use of the sub-optimal solution is not huge; however the topology can have a large effect on performance.  +
This paper considers the fundamental design and modeling of the Caltech ducted fan. The Caltech ducted fan is a scaled model of the longitudinal axis of a flight vehicle. The purpose of the ducted fan is the research and development of new nonlinear flight guidance and control techniques for Uninhabited Combat Aerial Vehicles. It is shown that critical design relations must be satisfied in order that the ducted fan's longitudinal dynamics behave similar to those of an flight vehicle. Preliminary flight test results illustrate the flying qualities of the ducted fan.  +
We consider the problem of attitude stabilization using exclusively visual sensory input, and we look for a solution which can satisfy the constraints of a ``bio-plausible'' computation. We obtain a PD controller which is a bilinear form of the goal image, and the current and delayed visual input. Moreover, this controller can be learned using classic neural networks algorithms. The structure of the resulting computation, derived from general principles by imposing a bilinear computation, has striking resemblances with existing models for visual information processing in insects (Reichardt Correlators and lobula plate tangential cells). We validate the algorithms using faithful simulations of the fruit fly visual input.  +
We consider the problem of purely visual pose stabilization (also known as servoing) of a second-order rigid- body system with six degrees of freedom: how to choose forces and torques, based on the current view and a memorized goal image, to steer the pose towards a desired one. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. This particular computational structure has several numerically favorable characteristics (sparse, local, and parallel), and thus permits an efficient engineering implementation. We show results of the control law tested on an indoor helicopter platform.  +
We consider the problem of purely visual pose stabilization of a second-order rigid-body system: how to choose forces and torques, based on the visual input alone, such that the view converges to a memorized goal image. Emphasis has been given to the bio-plausibility of the computation, in the sense that the control laws could be in principle implemented on the neural substrate of simple insects. We show that stabilizing laws can be realized by bilinear/quadratic operations on the visual input. Moreover, the control laws can be ``bootstrapped'' (learned unsupervisedly) from experience, which further substantiate the bio-plausibility of such computation.  +
Much of the progress in developing our ability to successfully design genetic circuits with predictable dynamics has followed the strategy of molding biological systems to fit into conceptual frameworks used in other disciplines, most notably the engineering sciences. Because biological systems have fundamental differences from systems in these other disciplines, this approach is challenging and the insights obtained from such analyses are often not framed in a biologically-intuitive way. Here, we present a new theoretical framework for analyzing the dynamics of genetic circuits that is tailored towards the unique properties associated with biological systems and experiments. Our framework approximates a complex circuit as a set of simpler circuits, which the system can transition between by saturating its various internal components. These approximations are connected to the intrinsic structure of the system, so this representation allows the analysis of dynamics which emerge solely from the system’s structure. Using our framework, we analyze the presence of structural bistability in a leaky autoactivation motif and the presence of structural oscillations in the Repressilator.  +
The bootstrapping problem consists in designing agents that laern a model of themsleves and the world, and utilize it to achieve useful tasks. It is different from other learning problems as the agent starts with uninterpreted observaions and commands, and with minimal prior information about the world. In this paper, we give a mathematical formalizatoin of this aspect of the problem. We argue that the vague constraint of having âno prior informationâ can be recast as a precise algebraic condition on the agent: that its behavior is invariant to particular classes of nuisances on the world, which we show can be well represented by actions of groups (diffeomorphisms, permutatations, linear transformations) on observations and commands. We then introduce the class of bilinear gradient dynamics sensors (DGDS) as a candidate for learning generic rootic sensorimotor cascades. We show how framing the problem as rejections of group nuisances allows a compact and modular analysis of typical preprocessing stages, such as learning the toplogy of sensors. We demonstrate learning and using such models on real-world range-finder and camera data from publicly available datasets.  +
In this paper we are concerned with the challenge of flight control of computationally-constrained micro-aerial vehicles that must rely primarily on vision to navigate confined spaces. We turn to insects for inspiration. We demonstrate that it is possible to control a robot with inertial, flight-like dynamics in the plane using insect-inspired visual autocorrelators or âelementary motion detectorsâ (EMDs) to detect patterns of visual optic flow. The controller, which requires minimal computation, receives visual information from a small omnidirectional array of visual sensors and computes thrust outputs for a fan pair to stabilize motion along the centerline of a corridor. To design the controller, we provide a frequency- domain analysis of the response of an array of correlators to a flat moving wall. The model incorporates the effects of motion parallax and perspective and provides a means for computing appropriate inter-sensor angular spacing and visual blurring. The controller estimates the state of robot motion by decomposing the correlator response into harmonics, an analogous operation to that performed by tangential cells in the fly. This work constitutes the first-known demonstration of control of non-kinematic inertial dynamics using purely correlators.  +
To contribute to efforts of bringing formal design-by-contract methods to hybrid systems, we introduce a variant of modal interface contract theory based on input/output automata with guarded transitions. We present an algebra of operators for interface composition, contract composition, contract conjunction, contract refinement and some theorems demonstrating that our contract object has reasonably universal semantics. As an application, we apply our framework to the design of a networked control systems of traffic.  +
Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two-input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single-cell responses that translated into analog population responses. Furthermore, when single-cell genetic states were aggregated into population-level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub-populations could be used to deduce order, timing, and duration of transient chemical events.  +
A reactive safety mode is built into a robust model predictive control algorithm for uncertain nonlinear systems with bounded disturbances. The algorithm enforces state and control constraints and blends two modes: (I) standard, guarantees re-solvability and asymptotic convergence in a robust receding-horizon manner; (II) safety, if activated, guarantees containment within an invariant set about a reference. The reactive safety mode provides robustness to unexpected, but real-time anticipated, state-constraint changes during standard mode operation. The safety-mode control policy is designed offline and can be activated at any arbitrary time. The standard-mode control has feedforward and feedback components: feedforward is from online solution of a finite-horizon optimal control problem; feedback is designed offline to provide robustness to system uncertainty and disturbances and to establish an invariant âstate tubeâ that guarantees standard-mode re-solvability at any time. The algorithm design is shown for a class of systems with incrementally-conic uncertain/nonlinear terms and bounded disturbances.  +
Stochasticity plays an essential role in biochemical systems. Stochastic behaviors of bimodality, excitability, and fluctuations have been observed in biochemical reaction networks at low molecular numbers. Stochastic dynamics can be captured by modeling the system using a forward Kolmogorov equation known in the biochemical literature as the chemical master equation. The chemical master equation describes the time evolution of the probability distributions of the molecule species. We develop a stochastic framework for the design of these time evolving probability distributions that includes specifying their uni-/multi-modality, their first moments, and their rate of convergence to the stationary distribution. By solving the corresponding optimizations programs, we determine the reaction rates of the biochemical systems that satisfy our design specifications. We then apply the design framework to examples of biochemical reaction networks to illustrate its strengths and limitations.  +
We derive phenomenological models of gene expression from a mechanistic description of chemical reactions using an automated model reduction method. Using this method, we get analytical descriptions and computational performance guarantees to compare the reduced dynamics with the full models. We develop a new two-state model with the dynamics of the available free ribosomes in the system and the protein concentration. We show that this new two-state model captures the detailed mass-action kinetics of the chemical reaction network under various biologically plausible conditions on model parameters. On comparing the performance of this model with the commonly used mRNA transcript-protein dynamical model for gene expression, we analytically show that the free ribosome and protein model has superior error and robustness performance.  +
Substantial reductions in aircraft size are possible if shorter, more aggressive, serpentine inlet ducts are used for low-observability constrained propulsion installations. To obtain this benefit, both inlet separation and compressor stall dynamics must be controlled. In this paper the integrated control of this coupled inlet/compression system is considered. Initial results are shown using separation point actuation to control both separation and stall dynamics. Calculations show that separation can be substantially reduced with approximately 1.2% core flow, based on scaling previous results. Simulation results using a medium fidelity model show that proportional control of distortion has little effect on stall behavior.  +
This paper presents preliminary results on the use of low flow, high momentum, pulsed air injectors to control the onset of stall in a low-speed, axial flow compressor. By measuring the unsteady pressures in front of the rotor, the controller determines the magnitude and phase of a stall cell and controls the injection of air in front of the rotor face. Initial experimental results have verified that controller slightly extends the stall point of the compressor and virtually eliminates the hysteresis loop normally associated with stall. An explanation of this effect is proposed based on the quasi-steady effects of air injection on the compressor characteristic curve.  +
This paper presents the use of pulsed air injection to control the onset of rotating stall in a low-speed, axial flow compressor. By measuring the unsteady pressures near the rotor face, a control algorithm determines the magnitude and phase of the first mode of rotating stall and controls the injection of air in the front of the rotor face. Experimental results show that this technique slightly extends the stall point of the compressor and eliminates the hysteresis loop normally associated with rotating stall. A parametric study is used to determine the optimal control parameters for suppression of stall. Analytic results---using a low-dimensional model developed by Moore and Greitzer combined with an unsteady shift in the compressor characteristic to model the injectors---give further insights into the operation of the controller. Based on this model, we show that the behavior of the experiment can be explained as a change in the bifurcation behavior of the system under nonlinear feedback. A higher fidelity simulation model is then used to further verify some of the specific performance characteristics that are observed in experiments.  +
We develop a system for implementing “packet-based” intercellular communication in an engineered bacterial population via conjugation. Our system uses gRNA-based identification markers that allow messages to be addressed to specific strains via Cas9-mediated cleavage of messages sent to the wrong recipient, which we show reduces plasmid transfer by four orders of magnitude. Integrase-mediated editing of the address on the message plasmid allows cells to dynamically update the message’s recipients in vivo. As a proof-of-concept demonstration of our system, we propose a linear path scheme that would propagate a message sequentially through the strains of a population in a defined order.  +
In this paper, we provide tools for convergence and performance analysis of an agreement protocol for a network of integrator agents with directed information flow. We also analyze algorithmic robustness of this consensus protocol for networks with mobile nodes and switching topology. A connection is established between the Fiedler eigenvalue of the graph Laplacian and the performance of this agreement protocol. We demon- strate that a class of directed graphs, called balanced graphs, have a crucial role in solving average-consensus problems. Based on the properties of balanced graphs, a group disagreement function (i.e. Lyapunov function) is proposed for convergence analysis of this agreement protocol for networks with directed graphs and switching topology.  +
This paper describes the implementation and testing of Alice, the California Institute of Technology’s entry in the 2005 DARPA Grand Challenge. Alice utilizes a highly networked control system architecture to provide high performance, autonomous driving in unknown en- vironments. Innovations include a vehicle architecture designed for efficient testing in harsh environments, a highly sensory-driven approach to fuse sensor data into speed maps used by real-time trajectory optimization algorithms, health and contingency management algorithms to manage failures at the component and system level, and a software logging and display envi- ronment that enables rapid assessment of performance during testing. The system successfully completed several runs in the National Qualifying Event, but encountered a combination of sens- ing and control issues in the Grand Challenge Event that led to a critical failure after traversing approximately 8 miles.  +
Modern aircraft increasingly rely on electric power for sub- systems that have traditionally run on mechanical power. The complexity and safety-criticality of aircraft electric power systems have therefore increased, rendering the design of these systems more challenging. This work is mot vated by the potential that correct-by-construction reactive controller synthesis tools may have in increasing the effectiveness of the electric power system design cycle. In particular, we have built an experimental hardware platform that captures some key elements of aircraft electric power systems within a simplified setting. We intend to use this plat- form for validating the applicability of theoretical advances in correct-by-construction control synthesis and for study- ing implementation-related challenges. We demonstrate a simple design workflow from formal specifications to auto- generated code that can run on software models and be used in hardware implementation. We show some preliminary results with different control architectures on the developed hardware testbed.  +
A numerical algorithm for computing necessary conditions for performance specifications is developed for nonlinear uncertain systems. The algorithm is similar in nature and behavior to the power algorithm for the mu lower bound, and doesn't rely on a descent method. The algorithm is applied to a practical example.  +
In this work we consider a class of networked control systems (NCS) when the control signal is sent to the plant via a UDP-like communication protocol. In this case the controller sends a communication packet to the plant across a lossy network, but the controller does not receive any acknowledgement signal indicating the status of the control packet. Standard observer based estimators assume the estimator has knowledge of what control signal is applied to the plant. Under the UDP-like protocol the controller/estimator does not have explicit knowledge whether the control signals have been applied to the plant or not. We present a simple estimation algorithm that consists of a state and mode observer as well as a constraint on the control signal sent to the plant. For the class of systems considered, discrete time LTI plants where at least one of the states that is directly affected by the input is also part of the measurement vector, the estimator is able to recover the fate of the control packet from the measurement at the next timestep and exhibit better performance than other naive schemes. For single-input-single-output (SISO) systems we are able to show convergence properties of the estimation error and the state. Simulations are provided to demonstrate the algorithm and show it's effectiveness.  +
Experimental comparisons between four different control design methodologies are applied to a small vectored thrust engine. Each controller is applied to three trajectories of varying aggressiveness. The control strategies considered are LQR, H_infty, gain scheduling, and feedback linearization. The experiments show that gain scheduling is essential to achieving good performance. The strengths and weaknesses of each methodology are also examined.  +
Controllers developed for control of flexible-link robots in hybrid force-position control tasks by a new singular perturbation analysis of flexible manipulators are implemented on an experimental two-robot grasping setup. Various performance criteria are set up and experimental results are discussed within that setting to show tradeoffs in using flexible link robots for grasping. We conclude that large flexibility can be controlled without too much additional effort, has performance comparable to rigid robots and possesses enhancing properties which make it attractive for use in certain types of applications.  +
In this paper, we develop an experimentally val- idated MATLAB software toolbox as an accompaniment to an in vitro cell-free biomolecular “breadboard” system. The toolbox gives insight into the dynamics of unmeasured states in the cell-free system, accounting especially for the resource usage. Parameter lumping and the reduced order modeling are used to maintain computational tractability and to avoid ill-conditioning. The toolbox allows for most applications to be implemented with standard set of commands for ease of use. Due to the breadboarding nature of the underlying cell-free sys- tem, the toolbox provides a general framework for experiment planning and predictive modeling for synthetic biomolecular circuits cell-free systems, accelerating our capacity to rationally design circuits from well characterized parts.  +
In this paper, we consider the problem of synthesizing correct-by-construction controllers for discrete-time dynamical systems. A commonly adopted approach in the literature is to abstract the dynamical system into a finite transition system (FTS) and thus convert the problem into a two player game between the environment and the system on the FTS. The controller design problem can then be solved using synthesis tools for general linear temporal logic or generalized reactivity(1) (GR1) specifications. In this article, we propose a new abstraction algorithm. Instead of generating a single FTS to represent the system, we generate two FTSs, which are underand over-approximations of the original dynamical system. We further develop an iterative abstraction scheme by exploiting the concept of winning sets, i.e., the sets of states for which there exists a winning strategy for the system. Finally, the e�ciency of the new abstraction algorithm is illustrated by numerical examples.  +
Biomolecular circuits with two distinct and stable steady states have been identified as essential components in a wide range of biological networks, with a variety of mechanisms and topologies giving rise to their important bistable property. Understanding the differences between circuit implementations is an important question, particularly for the synthetic biologist faced with determining which bistable circuit design out of many is best for their specific application. In this work we explore the applicability of Sturm's theorem—a tool from nineteenth-century real algebraic geometry—to comparing ‘functionally equivalent’ bistable circuits without the need for numerical simulation. We first consider two genetic toggle variants and two different positive feedback circuits, and show how specific topological properties present in each type of circuit can serve to increase the size of the regions of parameter space in which they function as switches. We then demonstrate that a single competitive monomeric activator added to a purely monomeric (and otherwise monostable) mutual repressor circuit is sufficient for bistability. Finally, we compare our approach with the Routh–Hurwitz method and derive consistent, yet more powerful, parametric conditions. The predictive power and ease of use of Sturm's theorem demonstrated in this work suggest that algebraic geometric techniques may be underused in biomolecular circuit analysis.  +
We present an automated model reduction algorithm that uses quasi-steady state approximation based reduction to minimize the error between the desired outputs. Additionally, the algorithm minimizes the sensitivity of the error with respect to parameters to ensure robust performance of the reduced model in the presence of parametric uncertainties. We develop the theory for this model reduction algorithm and present the implementation of the algorithm that can be used to perform model reduction of given SBML models. To demonstrate the utility of this algorithm, we consider the design of a synthetic biological circuit to control the population density and composition of a consortium consisting of two different cell strains. We show how the model reduction algorithm can be used to guide the design and analysis of this circuit.  +
This paper presents a mathematical model for a synthetic transcriptional regulatory network in vitro. This circuit design resembles one of the well-known network motifs, the inco- herent feed-forward loop, in which an activator regulates both a gene and a repressor of the gene. Through mathematical analysis, we show how the circuit can be controlled to demonstrate exact adaptation to input signals.  +
Designing genetic circuits to control the behaviors of microbial populations is an ongoing challenge in synthetic biology. Here we analyze circuits which implement dosage control by controlling levels of a global signal in a microbial population in face of varying cell density, growth rate, and environmental dilution. We utilize the Lux quorum sensing system to implement dosage control circuits, and we analyze the dynamics of circuits using both simplified analytical analysis and in silico simulations. We demonstrate that strong negative feedback through inhibiting LuxI synthase expression along with AiiA degradase activity results in circuits with fast response times and robustness to cell density and dilution rate. We find that degradase activity yields robustness to variations in population density for large population sizes, while negative feedback to synthase production decreases sensitivity to dilution rates.  +
This paper provides preliminary work in an aim to fundamentally understand the effects of temperature fluctuations in the dynamics of biological oscillators. Motivated by circadian rhythms, we are interested in understanding how time-varying temperatures might play a role in the properties of biochemical oscillators. This paper investigates time-dependent Arrhenius scaling of biochemical networks with delays. We assume these time-delays arise from a sequence of simpler reactions that can be modeled as an aggregate delay. We focus on a model system, the Goodwin oscillator, in which we use time-varying rate coefficients as a mechanism to understand the possible effects of temperature fluctuations. The emergence of delays from a sequence of reactions can be better understood through the Goodwin model. For a high order system and comparably high reaction rates, one can approximate the large sequence of reactions in the model with a delay, which can be interpreted as the time needed to go through the âqueueâ. Such types of delays can arise in the process of transcription for example. To study how these delays are affected by temperature fluctuations, we take the limit as the order of the system and the mean reaction rates approach infinity with a periodically time-varying rate coefficient. We show that the limit cycle of the Goodwin oscillator varies only in the limit when the oscillator frequency is much larger than the frequency of temperature oscillations. Otherwise, the instantaneous frequency of the oscillator is dominated by the mean value of the time-varying temperature.  +
We present a mathematical reconstruction of the kinematics and dynamics of flight initiation as observed in high-speed video recordings of the insect Drosophila melanogaster. The behavioral dichotomy observed in the fruit flies' flight initiation sequences, as a response to different stimuli, was reflected in two contrasting sets of dynamics once the flies had become airborne. By reconstructing the dynamics of unconstrained motion during flight initiations, we assess the fly's responses (generation of forces and moments) amidst these two dynamic patterns. Moreover, we introduce a 3D visual tracking algorithm as a tool to analyze the wing kinematics applied by the insect, and investigate their relation(s) to the production of these aerodynamic forces. Using this framework we formulate different hypotheses about the modulation of flight forces and moments during flight initiation as a way torefining our understanding of insect flight control.,  +
Gene expression is often controlled by natural genetic regulatory networks that govern the rates at which genes are transcribed. Recent work has shown that synthetic versions of genetic networks can be designed and built in living cells. Applications for these synthetic regulatory networks include intracellular decision-making and computation. In this study, we propose a new synthetic genetic network that behaves as a digital clock, producing square waveform oscillations. We analyze two models of the network, a deterministic model based on Michaelis-Menten kinetics, as well as a stochastic model based on the Gillespie algorithm. Both models predict regions of oscillatory behavior; the deterministic model provides insight into the conditions required to produce the oscillating clock-like behavior, while the stochastic model is truer to natural dynamics. Intracellular stochasticity is seen to contribute phase noise to the oscillator, and we propose improvements for the network and discuss the conceptual foundations of these improvements.  +
We study the dynamic and static input output behavior of several primitive genetic interactions and their e↵ect on the performance of a genetic signal di↵erentiator. In a simplified design, several requirements for the linearity and time-scales of processes like transcription, translation and competitive promoter binding were introduced. By ex- perimentally probing simple genetic constructs in a cell-free experimental environment and fitting semi-mechanistic models to these data, we show that some of these require- ments can be verified, while others are only met with reservations in certain operational regimes. Analyzing the linearized model of the resulting genetic network we conclude that it approximates a di↵erentiator with relative degree one. Taking also the discovered non-linearities into account and using a describing function approach, we further deter- mine the particular frequency and amplitude ranges where the genetic di↵erentiator can be expected to behave as such.  +
We have developed a new course as well as an undergraduate minor in Control and Dynamical Systems for teaching design and analysis of feedback systems to students from diverse fields such as biology, computer science, and economics as well as all traditional engineering %disciplines.  +
In this paper we discuss the application of correct-by-construction techniques to a resilient, risk-aware software architecture for onboard, real-time autonomous operations. We mean to combat complexity and the accidental introduction of bugs through the use of verifiable auto-coding software and correct-by-construction techniques, and discuss the use of a toolbox for correct-by-construction Temporal Logic Planning (TuLiP) for such a purpose. We describe some of TuLiPâs current functionality, specifically its ability to model symbolic discrete systems and synthesize software controllers and control policies that are correct-by-construction. We then move on to discuss the use of these techniques to define a deliberative goal-directed executive capability that performs risk-informed action-planning â to satisfy the mission goals (specified by mission control) within the specified priorities and constraints. Finally, we discuss an application of the TuLiP process to a simple rover resilience scenario.  +
The Goursat normal form theorem gives conditions under which an Pfaffian exterior differential system is equivalent to a certain normal form. This paper details how the Goursat normal form and its extensions provide a unified framework for understanding feedback linearization, chained form, and differential flatness. <p> Keywords: Exterior differential systems, nonholonomic constraints, chained form, feedback linearization, differentially flat.  +
We analyze the performance of an approximate distributed Kalman filter proposed in recent work on distributed coordination. This approach to distributed estimation is novel in that it admits a systematic analysis of its performance as various network quantities such as connection density, topology, and bandwidth are varied. Our main contribution is a frequency-domain characterization of the distributed estimator's steady-state performance; this is quantified in terms of a special matrix associated with the connection topology called the graph Laplacian, and also the rate of message exchange between immediate neighbors in the communication network.  +
This paper describes algorithms to generate trajectories for differentially flat systems with zero dynamics. Zero dynamics in flat systems occur when the flat outputs are not the tracking outputs. This means that the output trajectories can be fully parametrized by the flat outputs, but that there is some additional freedom left. This freedom can be exploited to minimize a cost criterion. We parametrize the differentially flat outputs by basis functions, and solve for the parameters so as to track a prescribed trajectory approximately while minimizing a cost function. We focus on implementation issues and point out the computational cost involved in the various problems.  +
In this paper, we approximate models of interconnected systems that are to be used for decentralized control design. The suggested approach is based on approximation of so-called subnetwork models. A subnetwork model is a model of the interconnected system, as seen from one specific position in the network. The simplification is done by using weighted model reduction, and several approximation criteria are given. A new method for weighted model reduction is used. The method is based on a combination of known techniques that use semidefinite programming and frequency-data samples of transfer functions. The method is guaranteed to preserve stability and does not depend strongly on the order of the original model. This is particularly important for large interconnected systems. Two examples are given to illustrate the technique.  +
any interesting control systems are mechanical control systems. In spite of this, there has not been much effort to develop methods which use the special structure of mechanical systems to obtain analysis tools which are suitable for these systems. In this dissertation we take the first steps towards a methodical treatment of mechanical control systems. <p> First we develop a framework for analysis of certain classes of mechanical control systems. In the Lagrangian formulation we study ``simple mechanical control systems'' whose Lagrangian is ``kinetic energy minus potential energy.'' We propose a new and useful definition of controllability for these systems and obtain a computable set of conditions for this new version of controllability. We also obtain decompositions of simple mechanical systems in the case when they are not controllable. In the Hamiltonian formulation we study systems whose control vector fields are Hamiltonian. We obtain decompositions which describe the controllable and uncontrollable dynamics. In each case, the dynamics are shown to be Hamiltonian in a suitably general sense. <p> Next we develop intrinsic descriptions of Lagrangian and Hamiltonian mechanics in the presence of external inputs. This development is a first step towards a control theory for general Lagrangian and Hamiltonian control systems. Systems with constraints are also studied. We first give a thorough overview of variational methods including a comparison of the ``nonholonomic'' and ``vakonomic'' methods. We also give a generalised definition for a constraint and, with this more general definition, we are able to give some preliminary controllability results for constrained systems.  +
Robustness to temperature variation is an important specification in biomolecular circuit design. While the cancellation of parametric temperature dependencies has been shown to improve the temperature robustness of the period in a synthetic oscillator design, the performance of other biomolecular circuit designs in different temperature conditions is relatively unclear. Using a combination of experimental measurements and mathematical models, we assessed the temperature robustness of two biomolecular circuit motifs—a negative feedback loop and a feedforward loop. We found that the measured responses of both the circuits changed with temperature, both in the amplitude and in the transient response. We also found that, in addition to the cancellation of parametric temperature dependencies, certain parameter regimes could facilitate the temperature robustness of the negative feedback loop, although at a performance cost. We discuss these parameter regimes in the context of the measured data for the negative feedback loop. These results should help develop a framework for assessing and designing temperature robustness in biomolecular circuits.  +
Distributed algorithms for averaging have attracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks.....  +
Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System (MDS), developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a software algorithm for converting goal network control programs into linear hybrid systems is described. The conversion process is a bisimulation; the resulting linear hybrid system can be verified for safety in the presence of failures using existing symbolic model checkers, and thus the original goal network is verified. A moderately complex goal network control program is converted to a linear hybrid system using the automatic conversion software and then verified.  +
We propose a methodology for automatic synthesis of embedded control software that accounts for exogenous disturbances. The resulting system is guaranteed, by construction, to satisfy a given specification expressed in linear temporal logic. The embedded control software consists of three components: a goal generator, a trajectory planner, and a continuous controller. We demonstrate the effectiveness of the proposed technique through an example of an autonomous vehicle navigating an urban environment. This example also illustrates that the system is not only robust with respect to exogenous disturbances but also capable of handling violation of the environment assumptions.  +
We develop a method for the control of discrete-time nonlinear systems subject to temporal logic specifications. Our approach uses a coarse abstraction of the system and an automaton representing the temporal logic specification to guide the search for a feasible trajectory. This decomposes the search for a feasible trajectory into a series of constrained reachability problems. Thus, one can create controllers for any system for which techniques exist to compute (approximate) solutions to constrained reachability problems. Representative techniques include sampling-based methods for motion planning, reachable set computations for linear systems, and graph search for finite discrete systems. Our approach avoids the expensive computation of a discrete abstraction, and its implementation is amenable to parallel computing. We demonstrate our approach with numerical experiments on temporal logic motion planning problems with high-dimensional (10+ states) continuous systems.  +
The development of autonomous vehicles for urban driving has seen rapid progress in the past 30 years. This paper provides a summary of the current state of the art in autonomous driving in urban environments, based primarily on the experiences of the authors in the 2007 DARPA Urban Challenge (DUC). The paper briefly summarizes the approaches that different teams used in the DUC, with the goal of describing some of the challenges that the teams faced in driving in urban environments. The paper also highlights the long term research challenges that must be overcome in order to enable autonomous driving and points to opportunities for new technologies to be applied in improving vehicle safety, exploiting intelligent road infrastructure and enabling robotic vehicles operating in human environments.  +
This report presents techniques for using discrete finite rotations to reorient a spacecraft from a given initial attitude to a final attitude which satisfies a specified aiming objective. The objective may be a fully specified final orientation or it may require that the spacecraft direct an instrument along a certain direction. Constraints are also imposed on the allowable intermediate orientations that the spacecraft may assume during the course of the maneuver, representing the operational requirements of onboard instrumentation. The algorithms presented consider solutions that will achieve the desired objective with only one or two slew maneuvers, although they may be easily extended to consider more complicated solutions requiring additional maneuvers.  +
B
This paper considers the problem of synthesizing correct-by-construction robotic controllers in environments with uncertain but fixed structure. âEnvironmentâ has two notions in this work: a map or âworldâ in which some controlled agent must operate and navigate (i.e. evolve in a configuration space with obstacles); and an adversarial player that selects con- tinuous and discrete variables to try to make the agent fail (as in a game). Both the robot and the environment are subjected to behavioral specifications expressed as an assume-guarantee linear temporal logic (LTL) formula. We then consider how to efficiently modify the synthesized controller when the robot encounters unexpected changes in its environment. The crucial insight is that a portion of this problem takes place in a metric space, which provides a notion of nearness. Thus if a nominal plan fails, we need not resynthesize it entirely, but instead can âpatchâ it locally. We present an algorithm for doing this, prove soundness, and demonstrate it on an example gridworld.  +
Wound healing is a complicated biological process consisting of many types of cellular dynamics and functions regulated by chemical and molecular signals. Recent advances in synthetic biology have made it possible to predictably design and build closed-loop controllers that can function appropriately alongside biological species. In this paper we develop a simple dynamical population model mimicking the sequential relay-like dynamics of cellular populations involved in the wound healing process. Our model consists of four nodes and five signals whose parameters we can tune to simulate various chronic healing conditions. We also develop a set of regulator functions based on type-1 incoherent feed forward loops (IFFL) that can sense the change from acute healing to incomplete chronic wounds, improving the system in a timely manner. Both the wound healing and type-1 IFFL controller architectures are compatible with available synthetic biology experimental tools for potential applications.  +
Nonlinear qualitative analysis is performed on the Moore-Greitzer model to evaluate the tradeoff of fluid noise, actuator magnitude saturation, bandwidth, rate limits, and the shape of compressor characteristics in active control of rotating stall in axial compressors with bleed valve actuators. Model order reduction is achieved by approximating the dynamics on the invariant manifold that captures the bifurcations and instabilities. Bifurcations and qualitative dynamics are obtained by analyzing the reduced system. The operability enhancement is defined as the extension of operating range for which fully developed rotating stall is avoided. Analytic formulas are derived for the operability enhancement as a function of noise level, actuator saturation limits, and the shape of the compressor characteristic, which is the major nonlinearity in the model. The shape of the compressor characteristic, especially the unstable part, is critical to the rate required for robust operability near the peak for the closed loop system. Experiments are carried out on a single-stage low-speed axial compressor using different level of steady air injections to generate different compressor characteristics. The theoretical formulas give good qualitative estimates to experimental data and simulations using a high fidelity model (37 states).  +
Insects exhibit incredibly robust closed loop flight dynamics in the face of uncertainties. A fundamental principle contributing to this unparalleled behavior is rapid processing and convergence of visual sensory information to flight motor commands via spatial wide-field integration, accomplished by retinal motion pattern sensitive interneurons (LPTCs) in the lobula plate portion of the visual ganglia. Within a control-theoretic framework, an inner product model for wide-field integration of retinal image flow is developed, representing the spatial decompositions performed by LPTCs in the insect visuomotor system. A rigorous characterization of the information available from this visuomotor convergence technique for motion within environments exhibiting non-omogeneous spatial distributions is performed, establishing the connection between retinal motion sensitivity shape and closed loop behavior. The proposed output feedback methodology is shown to be sufficient to give rise to experimentally observed insect navigational heuristics, including forward speed regulation, obstacle avoidance, hovering, and terrain following behaviors. Hence, extraction of global retinal motion cues through computationally efficient wide-field integration process- ing provides a novel and promising methodology for utilizing visual sensory information in autonomous robotic navigation and flight control applications.  +
Biochemical interactions in systems and synthetic biology are often modeled with Chemical Reaction Networks (CRNs). CRNs provide a principled modeling environment capable of expressing a huge range of biochemical processes. In this paper, we present a software toolbox, written in python, that complies high-level design specifications to CRN representations. This compilation process offers three advantages. First, the building of the actual CRN representation is automatic and outputs Systems Biology Markup Language (SBML) models compatible with numerous simulators. Second, a library of modular biochemical components allows for different architectures and implementations of biochemical circuits to represented succinctly with design choices propogated throughout the underlying CRN automatically. This prevents the often occurring mismatch between high-level designs and model dynamics. Third, high-level design specification can be embedded into diverse biomolecular environments, such as cell-free extracts and in vivo milieus. With these advantages offered by BioCRNpyler, users can quickly build and test multitude of models in different environments. Finally, our software toolbox has a parameter database, which allows users to rapidly prototype large models using very few parameters which can be customized later.  +
We present a detailed dynamical model of the behavior of transcription-translation circuits in vitro that makes explicit the roles played by essential molecular resources. A set of simple two-gene test circuits operating in a cell-free biochemical âbreadboardâ validate this model and highlight the consequences of limited resource availability. In particular, we are able to confirm the existence of biomolecular âcrosstalkâ and isolate its individual sources. The implications of crosstalk for biomolecular circuit design and function are discussed.  +
Synthetic gene expression is highly sensitive to intragenic compositional context (promoter structure, spacing regions between promoter and coding sequences, and ribosome binding sites). However, much less is known about the effects of intergenic compositional context (spatial arrangement and orientation of entire genes on DNA) on expression levels in synthetic gene networks. We compare expression of induced genes arranged in convergent, divergent, or tandem orientations. Induction of convergent genes yielded up to 400% higher expression, greater ultrasensitivity, and dynamic range than divergent- or tandem-oriented genes. Orientation affects gene expression whether one or both genes are induced. We postulate that transcriptional interference in divergent and tandem genes, mediated by supercoiling, can explain differences in expression and validate this hypothesis through modeling and in vitro supercoiling relaxation experiments. Treatment with gyrase abrogated intergenic context effects, bringing expression levels within 30% of each other. We rebuilt the toggle switch with convergent genes, taking advantage of supercoiling effects to improve threshold detection and switch stability.  +
In this paper, we investigate pre-orders for reason- ing about input-to-state stability properties of hybrid systems. We define the notions of uniformly continuous input simulations and bisimulations, which extend the notions in previous work to include inputs. We show that uniformly continuous input bisimulations preserve incremental input-to-state stability of hybrid systems, and thus provide a basis for constructing abstractions for verification. We show that Lyapunov function based input-to-state stability analysis can be cast in our frame- work as constructing a simpler one-dimensional system, using a uniformly continuous input simulation, which is input-to-state stable, and thus, inferring the input-to-state stability of the original system.  +
Molecular feedback control circuits can improve robustness of gene expression at the single cell-level. This achievement can be offset by requirements of rapid protein expression, that may induce cellular stress, known as burden, that reduces colony growth. To begin to address this challenge we take inspiration by ‘division-of-labor’ in heterogeneous cell populations: we propose to combine bistable switches and quorum sensing systems to coordinate gene expression at the population-level. We show that bistable switches in individual cells operating in parallel yield an ultrasensitive response, while cells maintain heterogeneous levels of gene expression to avoid burden across all cells. Within a feedback loop, these switches can achieve robust reference tracking and adaptation to disturbances at the population-level. We also demonstrate that molecular sequestration enables tunable hysteresis in individual switches, making it possible to obtain a wide range of stable population-level expressions.  +
We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior informa- tion, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a simple bioplausible control strategy. The convergence proper- ties of learning and control are demonstrated with extensive simulations and by analytical arguments.  +
Learning and adaptivity will play a large role in robotics in the future, as robots move from structured to unstructured environments that cannot be fully predicted or understood by the designer. Two questions that are open: 1) in principle, how much it is possible to learn; and, 2) in practice, how much we should learn. The bootstrapping scenario describes the extremum case where agents need to learn âeverythingâ from scratch, including a torque-to-pixels models for its robotic body. Systems with such capabilities will be advantaged in terms of being resilient to unforeseen changes and deviations from prior assumptions. This paper considers the bootstrapping problem for a subset of the set of all robots: the Vehicles, inspired by Braitenbergâs work, are idealization of mobile robots equipped with a set of âcanonicalâ exteroceptive sensors (camera; range- finder; field-sampler). Their sensel-level dynamics are derived and shown to be surprising close. We define the class of BDS models, which assume an instantaneous bilinear dynamics between observations and commands, and derive streaming-based bilinear strategies for them. We show in what sense the BDS dynamics approximates the set of Vehicles to guarantee success in the task of generalized servoing: driving the observations to a given goal snapshot. Simulations and experiments substantiate the theoretical results. This is the first instance of a bootstrapping agent that can learn the dynamics of a relatively large universe of systems, and use the models to solve well-defined tasks, with no parameter tuning or hand-designed features.  +
C
A cascade discrete-continuous state estimator design is presented for a class of monotone systems with both continuous and discrete state evolution. The proposed estimator exploits the partial order preserved by the system dynamics in order to satisfy two properties. First, its computation complexity scales with the number of variables to be estimated instead of scaling with the size of the discrete state space. Second, a separation principle holds: the continuous state estimation error is bounded by a monotonically decreasing function of the discrete state estimation error, the latter one converging to zero. A multi-robot example is proposed.  +
The bottom up design of genetic circuits to control cellular behavior is one of the central objectives within Synthetic Biology. Performing design iterations on these circuits in vivo is often a time consuming process, which has led to E. coli cell extracts to be used as simplified circuit prototyping environments. Cell extracts, however, display large batch-to-batch variability in gene expression. In this paper, we develop the theoretical groundwork for a model based calibration methodology for correcting this variability. We also look at the interaction of this methodology with the phenomenon of parameter (structural) non-identifiability, which occurs when the parameter identification inverse problem has multiple solutions. In particular, we show that under certain consistency conditions on the sets of output- indistinguishable parameters, data variability reduction can still be performed, and when the parameter sets have a cer- tain structural feature called covariation, our methodology may be modified in a particular way to still achieve the desired variability reduction.  +
Synthetic biologists have turned towards quorum systems as a path for building sophisticated microbial consortia that exhibit group decision making. Currently, however, even the most complex consortium circuits rely on only one or two quorum sensing systems, greatly restricting the available design space. High-throughput characterization of available quorum sensing systems is useful for finding compatible sets of systems that are suitable for a defined circuit architecture. Recently, cell-free systems have gained popularity as a test-bed for rapid prototyping of genetic circuitry. We take advantage of the transcription-translation cell-free system to characterize three commonly used Lux-type quorum activators, Lux, Las, and Rpa. We then compare the cell-free characterization to results obtained in vivo. We find significant genetic crosstalk in both the Las and Rpa systems and substantial signal crosstalk in Lux activation. We show that cell-free characterization predicts crosstalk observed in vivo.  +
In this work, we present modeling and experimental characterization of the minimum time needed for flipping of a DNA substrate by a two-integrase event detector. The event detector logic diâµerentiates the temporal order of two chemical inducers. We find that bundling biological rate parameters (transcription, translation, DNA search- ing, DNA flipping) into only a few rate constants in a stochastic model is sufficient to accurately predict final DNA states. We show, through time course data in E.coli, that these modeling predictions are reproduced in vivo. We believe this model validation is critical for using integrase-based systems in larger circuits.  +
A central goal of synthetic biology is to engineer cellular behavior by engineering synthetic gene networks for a variety of biotechnology and medical applications. The process of engineering gene networks often involves an iterative âdesign-build-testâ cycle, whereby the parts and connections that make up the network are built, characterized and varied until the desired network function is reached. Many advances have been made in the design and build portions of this cycle. However, the slow process of in vivo characterization of network function often limits the timescale of the testing step. Cell-free transcription-translation (TX-TL) systems offer a simple and fast alternative to performing these characterizations in cells. Here we provide an overview of a cell-free TX-TL system that utilizes the native Escherichia coli TX-TL machinery, thereby allowing a large repertoire of parts and networks to be characterized. As a way to demonstrate the utility of cell-free TX-TL, we illustrate the characterization of two genetic networks: an RNA transcriptional cascade and a protein regulated incoherent feed-forward loop. We also provide guidelines for designing TX-TL experiments to characterize new genetic networks. We end with a discussion of current and emerging applications of cell free systems.  +
Previous work at Caltech has developed an air injection controller for rotating stall based on the idea of a shifting compressor characteristic. To further understand the properties of this controllers, a series of open loop tests were performed to measure the performance characteristics of an axial flow compression system when air was injected upstream of the rotor face. The distance from the rotor face, the span-wise position, and the angle relative to the mean axial flow were varied. These tests show that the injection of air has drastic effects on the stalling mass flow rate and on the size of the hysteresis loop associated with rotating stall. The stalling mass flow rate was decreased by 10\% and the hysteresis loop was completely eliminated under some conditions.  +
We develop the study of primitives of human motion, which we refer to as movemes. The idea is to understand human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. Where do these dynamic primitives come from in practice? How can we construct an alphabet of movemes from human data? In this paper we address these issues. We define conditions under which collections of signals are well-posed according to a dynamical model class M and thus can generate movemes. Using examples from human drawing data, we show that the definition of well-posedness can be applied in practice so to establish if sets of actions, reviewed as signals in time, can define movemes.  +
We describe a technique for the efficient computation of the dominant-scale dynamics of a fluid system when only a high-fidelity simulation is available. Such a technique is desirable when governing equations for the dominant scales are unavailable, when model reduction is impractical, or when the original high-fidelity computation is expensive. We adopt the coarse analysis framework proposed by I. G. Kevrekidis (Comm. Math. Sci. 2003), where a computational superstructure is designed to use short-time, high-fidelity simulations to extract the dominant features for a multi- scale system. We apply this technique to compute the dominant features of the compressible flow through a planar diffuser. We apply the proper orthogonal decomposition to classify the dominant and subdominant scales of diffuser flows. We derive a suitable coarse pro jective Adams-Bashforth time integration routine and apply it to compute averaged diffuser flows. The results include accu- rate tracking of the dominant-scale dynamics for a range of parameter values for the computational superstructure. These results demonstrate that coarse analysis methods are useful for solving fluid flow problems of a multiscale nature. <p> In order to elucidate the behavior of coarse analysis techniques, we make comparisons to averaging theory. To this end, we derive governing equations for the average motion of charged particles in a magnetic field in a number of different settings. First, we apply a novel procedure, inspired by WKB theory and Whitham averaging, to average the variational principle. The resulting equations are equivalent to the guiding center equations for charged particle motion; this marks an instance where averaging and variational principles commute. Secondly, we apply Lagrangian averaging techniques, previously applied in fluid mechanics, to derive averaged equations. Making comparisons to the WKB/Whitham-style derivation allows for the necessary closure of the Lagrangian averaging formulation. We also discuss the Hamiltonian setting and show that averaged Hamiltonian systems may be derivable using concepts from coarse analysis. Finally, we apply a prototypical coarse analysis procedure to the system of charged particles and generate tra jectories that resemble guiding center tra jectories. We make connections to perturbation theory to derive guidelines for the design of coarse analysis techniques and comment on the prototypical coarse analysis application.  
Standard schemes in system identification and adaptive control rely on persistence of excitation to guaran- tee parameter convergence. Inspired by networked systems, we extend parameter adaptation to the multi-agent setting by combining a gradient law with consensus dynamics. The gradient law introduces a learning signal, while consensus dynamics preferentially push each agentâs parameter estimates toward those of its neighbors. We show that the resulting online, decentralized parameter estimator combines local and neighboring information to identify the true parameters even if no single agent employs a persistently exciting input. We also elaborate upon collective persistence of excitation in networked adaptive algorithms.  +
Previous work at Caltech has developed a controller for rotating stall in axial flow compressors using pulsed air injection. In this work, theory is developed for the combination of this air injection controller with a bleed valve controller for the system's surge dynamics. The controller analysis is based on the surge dynamics acting on a slow time scale relative to the rotating stall dynamics. Experiments demonstrating this controller design on the Caltech rig are also presented.  +
In this paper we characterize the impact of imperfect communication on the performance of a decentralized mobile sensor network. We first examine and demonstrate the trade-offs between communication and sensing objectives, by determining the optimal sensor configurations when introducing imperfect communication. We further illustrate the performance degradation caused by non-ideal communication links in a decentralized mobile sensor network. To address this, we propose a decentralized motion-planning algorithm that considers communication effects. The algorithm is a cross-layer design based on the proper interface of physical and application layers. Simulation results will show the performance improvement attained by utilizing this algorithm.  +
In this paper we consider the impact of communication noise on distributed sensing and estimation in mobile networks. We characterize when a node should rely on getting information from others and when it should rely on self exploration. In doing so, we explore the trade-offs between sensing and communication by finding the optimum network configuration under communication constraints. We also show how to achieve the optimum configuration in a distributed manner. While our main results are presented in one dimension (1D), we provide insight into the two dimension (2D) setup and extend a number of key results to 2D.  +
We propose a compositional stability analysis methodology for verifying properties of systems that are interconnections of multiple subsystems. The proposed method assembles stability certificates for the interconnected system based on the certificates for the input-output properties of the subsystems. The hierarchy in the analysis is achieved by utilizing dual decomposition ideas in optimization. Decoupled subproblems establish subsystem level input-output properties whereas the ``master'' problem imposes and updates the conditions on the subproblems toward ensuring interconnected system level stability properties. Both global stabilityanalysis and region-of-attraction analysis are discussed.  +
This work is motivated by the problem of synthe- sizing mode sequences for continuous-time polynomial switched systems in order to guarantee that the trajectories of the system satisfy certain high-level specifications expressed in linear temporal logic. We use augmented finite transition systems as abstract models of continuous switched systems. Augmented finite transition systems are equipped with liveness properties that can be used to enforce progress in accordance with the underlying dynamics. We then introduce abstraction and refinement relations that induce a preorder on this class of finite transition systems. By construction, the resulting pre-order respects the feasibility (i.e., realizability) of the synthesis problem. Hence, existence of a discrete switching strategy for one of these abstract finite transition systems guarantees the existence of a mode sequence for the continuous system such that all of its trajectories satisfy the specification. We also present an algorithm, which can be implemented using sum-of-squares based relaxations, to compute such high fidelity abstract models in a computationally tractable way. Finally, these ideas are illustrated on an example.  +
In this paper we present a dynamical systems framework for analyzing multi-agent rendezvous problems and characterize the dynamical behavior of the collective system. Recently, the problem of rendezvous has been addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of the problem. The proposed approach is based on set invariance theory and focusses on how to generate feedback between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions of the agents and the dynamics is modeled as linear first order systems. The proposed framework however is not fundamentally limited to linear first order dynamics and can be extended to analyze rendezvous of higher order agents.  +
In this article is presented a dynamical systems framework for analysing multi-agent rendezvous problems and characterize the dynamical behaviour of the collective system. Recently, the problem of rendezvous has been addressed considerably in the graph theoretic framework, which is strongly based on the communication aspects of the problem. The proposed approach is based on the set invariance theory and focusses on how to generate feedback between the vehicles, a key part of the rendezvous problem. The rendezvous problem is defined on the positions of the agents and the dynamics is modelled as linear first-order systems. These algorithms have also been applied to non-linear first-order systems. The rendezvous problem in the framework of cooperative and competitive dynamical systems is analysed that has had some remarkable applications to biological sciences. Cooperative and competitive dynamical systems are shown to generate monotone flows by the classical Muller--Kamke theorem, which is analysed using the set invariance theory. In this article, equivalence between the rendezvous problem and invariance of an appropriately defined cone is established. The problem of rendezvous is cast as a stabilization problem, with a the set of constraints on the trajectories of the agents defined on the phase plane. The n-agent rendezvous problem is formulated as an ellipsoidal cone invariance problem in the n-dimensional phase space. Theoretical results based on set invariance theory and monotone dynamical systems are developed. The necessary and sufficient conditions for rendezvous of linear systems are presented in the form of linear matrix inequalities. These conditions are also interpreted in the Lyapunov framework using multiple Lyapunov functions. Numerical examples that demonstrate application are also presented.  +
In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this new version of controllability is also derived. This condition involves a new object which we call the symmetric product. Of particular interest is a definition of "equilibrium controllability" for which we are able to derive computable sufficient conditions. Examples illustrate the theory.  +
Lagrangian control systems that are differentially flat with flat outputs that only depend on configuration variables are said to be configuration flat. We provide a complete characterisation of configuration flatness for systems with $n$ degrees of freedom and $n-1$ controls whose range of control forces only depends on configuration but not on velocity and whose Lagrangian has the form of kinetic energy minus potential. The method presented allows us to determine if such a system is configuration flat and, if so provides a constructive method for finding all possible configuration flat outputs. Our characterisation relates configuration flatness to Riemannian geometry. We illustrate the method by two examples.  +
In this paper, we synthesize a robust connected cruise controller with performance guarantee using probabilis- tic model checking, for a vehicle that receives motion informa- tion from several vehicles ahead through wireless vehicle-to- vehicle communication. We model the car-following dynamics of the preceding vehicles as Markov chains and synthesize the connected cruise controller as a Markov decision process. We show through simulations that such a design is robust against imperfections in communication.  +
In this paper, we introduce a consensus protocol for a network of dynamic agents that allows the agents to reach a decision in a distributed and cooperative fashion. We consider both linear and nonlinear protocols as well as the characteristic function of the communication links in the network. This includes links with delay and (possible) distortion/filtering effects. It turns out that for a number of protocols, the convergence properties and the decision-value obtained via this protocol is strongly related to connectivity and algebraic graph theoretic properties of the information flow in the network of decision-making agents. Standard tools from multivariable control and linear control theory such as Nyquist plots appear naturally for convergence analysis of the obtained linear protocols. For the analysis of the nonlinear protocols, certain disagreement costs are constructed that are minimized by the consensus protocols in a distributed way. Simulation results are provided for attitude alignment of a group of 20 dynamic agents.  +
We consider the problem of average consensus seeking in networked multi-agent systems. Based on local information and a simple distributed algorithm, states of all agents automatically converge to the average value of the initial conditions, where the convergence speed is determined by the algebraic connectivity of the underlying communication network. In order to achieve an average consensus quickly, we propose a new type of consensus protocol, multi-hop relay protocol, in which each agent expands its knowledge by employing multi-hop communication links. We explicitly show that multi-hop relay protocol increases the convergence speed without physically changing the network topology. Moreover, accumulated delays along communication links are discussed. We show that, for multi-hop relay protocol, the faster the protocol converges, the more sensitive it is to the delay. This tradeoff is identified when we investigate the stable delay margin using frequency sweep method.  +
This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations.  +
In this paper, we discuss consensus problems for a network of dynamic agents with fixed and switching topologies. We analyze three cases: i) networks with switching topology and no time-delays, ii) networks with fixed topology and communication time-delays, and iii) max-consensus problems (or leader determination) for groups of discrete-time agents. In each case, we introduce a linear/nonlinear consensus protocol and provide convergence analysis for the proposed distributed algorithm. Moreover, we establish a connection between the Fiedler eigenvalue of the information flow in a network (i.e. algebraic connectivity of the network) and the negotiation speed (or performance) of the corresponding agreement protocol. It turns out that balanced digraphs play an important role in addressing average-consensus problems. We introduce disagreement functions that play the role of Lyapunov functions in convergence analysis of consensus protocols. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.  +
Station keeping and reorientation control of a cluster of fully-actuated low-thrust micro-satellites is considered in this paper. We address the control problem by taking advantage of the fully-actuated structure of the micro-satellite. We propose a very general open-loop solution by solving in real-time constrained trajectory generation problems for stationkeeping and reorientation. Performance of this methodology is reported for a typical micro-satellite format ion flying space mission using the Nonlinear Trajectory Generation software package.  +
We consider the problem of designing policies for Markov decision processes (MDPs) with dynamic coherent risk objectives and constraints. We begin by formulating the problem in a Lagrangian framework. Under the assumption that the risk objectives and constraints can be represented by a Markov risk transition mapping, we propose an optimization-based method to synthesize Markovian policies that lower-bound the constrained risk-averse problem. We demonstrate that the formulated optimization problems are in the form of difference convex programs (DCPs) and can be solved by the disciplined convex-concave programming (DCCP) framework. We show that these results generalize linear programs for constrained MDPs with total discounted expected costs and constraints. Finally, we illustrate the effectiveness of the proposed method with numerical experiments on a rover navigation problem involving conditional-value-at-risk (CVaR) and entropic-value-at-risk (EVaR) coherent risk measures.  +
We present a theory of contracts that is centered around reacting to failures and explore it from a general assume-guarantee perspective as well as from a concrete context of automated synthesis from linear temporal logic (LTL) specifications, all of which are compliant with a contract metatheory introduced by Benveniste et al. We also show how to obtain an automated procedure for synthesizing reactive assume-guarantee contracts and implementations that capture ideas like optimality and robustness based on assume-guarantee lattices computed from antitone Galois connection fixpoints. Lastly, we provide an example of a “reactive GR(1)” contract and a simulation of its implementation.  +
We consider a discrete time linear feedback control system with additive noise where the control signals are to be sent across a data link from the controller to the actuators. Due to network constraints it is desired to reduce the transmission frequency of the control signals. We show that by including a finite sequence of predicted control signals in each communication packet the frequency of transmission can be reduced by transmitting only when the previously sent sequence has run out. The price to pay is that the closed loop error will increase. We introduce a novel communication protocol, which we call Input Difference Transmission Scheme (IDTS), which transmits control packets when the difference between the newly computed control sequence and the predicted control sequence previously transmitted is larger than a certain thresh- old. This threshold is a design parameter and we show how the closed loop behavior varies with this threshold. Simulation results are provided to augment the theory and show how the protocol works.  +
In this paper, we consider a robust networked control problem. We consider linear unstable and uncertain discrete time plants with a network between the sensor and controller as well as between the controller and plant. We investigate the effect of data drop out in the form of packet losses and we focus on the tradeoff between packet arrival rate versus the uncertainties of the system dynamics. We show that the minimum packet arrival rate and the maximum uncertainty of the system dynamics have a positive correlation. Four distinct control schemes are explored and serve as examples to study this tradeoff. We derive sufficient condition for each scheme to ensure almost sure stability of the closed loop system. Simulation and examples are provided to assist the theory.  +
We present a set of primitive operations which forms the core of a robot system description and control language. The actions of the individual primitives are derived from the mathematical structure of the equations of motion for constrained mechanical systems. The recursive nature of the primitives allows composite robots to be constructed from more elementary daughter robots. We review a few pertinent results of classical mechanics, describe the functionality of our primitive operations, and present several different hierarchical strategies for the description and control of a two-fingered hand holding a box.  +
Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System (MDS), developed at the Jet Propulsion Laboratory, takes a goal-based control approach. A software algorithm for converting goal network control programs into linear hybrid systems exists and is a bisimulation; the resulting linear hybrid system can be verified for safety in the presence of failures using existing symbolic model checkers, and thus the original goal network is verified. A substantial example control program based on a proposed mission to Titan, a moon of Saturn, is converted using the procedures discussed.  +
Motivated by the desire to analyze high dimen- sional control systems without explicitly forming computation- ally expensive linear matrix inequality (LMI) constraints, we seek to exploit special structure in the dynamics matrix. By using Jordan algebraic techniques we show how to analyze continuous time linear dynamical systems whose dynamics are exponentially invariant with respect to a symmetric cone. This allows us to characterize the families of Lyapunov functions that suffice to verify the stability of such systems. We highlight, from a computational viewpoint, a class of systems for which stability verification can be cast as a second order cone program (SOCP), and show how the same framework reduces to linear programming (LP) when the system is internally positive, and to semidefinite programming (SDP) when the system has no special structure.  +
This survey aims to provide a general overview of relevant terms and resources for understanding the intersection of synthetic biology and control theory. A reader with a background in control theory should come away with a reasonable understanding of the current 24 state-of-the-art of biological system identification, controller design and implementation, and the open challenges facing the field. Additionally, this review updates and builds upon previous publications on this subject. As this particular work is limited to a selected number of topics, additional reviews are suggested throughout the text for deeper reading. In the following sections, each of the challenges is addressed within the typical workflow for control implementation of more traditionally engineered systems (Figure 1). Engineered biological systems present a number of challenges to all stages of this workflow for reasons such as limitations in real-time measurement, resource competition with the host organism, and incomplete knowledge of underlying biological processes. First, strategies for framing a biologi- cal organism as a system with defined inputs, outputs, sensors, actuators, and measurements are discussed (Figure 1a). Obtaining dynamic and reliable measurements within biological organisms is a daunting challenge, engineered or otherwise. An overview of the state-of-the-art tools for modeling and characterizing biological systems is presented, followed by system identification methods specifically designed for the types of data available from biological measurements. The difficulty in engineering complex genetic networks, combined with severe limitations in real- time measurement, means that the body of work for controller design (Figure 1b) is limited – as a result, we discuss the open problems and challenges awaiting the entrepreneurial reader, and also present a number of examples of feedback loop implementation in living cells (Figure 1c). Finally, the necessary challenges in synthetic biology and development of control theoretical frameworks that need to be addressed in order to advance the field are discussed.  
This tutorial describes TuLiP, the Temporal Logic Planning toolbox, a collection of tools for designing controllers for hybrid systems from specifications in temporal logic. The tools support a workflow that starts from a description of desired behavior, and of the system to be controlled. The system can have discrete state, or be a hybrid dynamical system with a mixed discrete and continuous state space. The desired behavior can be represented with temporal logic and discrete transition systems. The system description can include uncontrollable variables that take discrete or continuous values, and represent disturbances and other environmental factors that affect the dynamics, as well as communication signals that affect controller decisions. A control design problem is solved in phases that involve abstraction, discrete synthesis, and continuous feedback control. Abstraction yields a discrete description of system dynamics in logic. For piecewise affine dynamical systems, this abstraction is constructed automatically, guided by the geometry of the dynamics and under logical constraints from the specification. The resulting logic formulae describe admissible discrete behaviors that capture both controlled and environment variables. The discrete description resulting from abstraction is then conjoined with the desired logic specification. To find a controller, the toolbox solves a game of infinite duration. Existence of a discrete (winning) strategy for the controlled variables in this game is a proof certificate for the existence of a controller for the original problem, which guarantees satisfaction of the specification. This discrete strategy, concretized by using continuous controllers, yields a feedback controller for the original hybrid system. The toolbox frontend is written in Python, with backends in C, Python, and Cython. The tutorial starts with an overview of the theory behind TuLiP, and of its software architecture, organized into specifi- cation frontends and backends that implement algorithms for abstraction, solving games, and interfaces to other tools. Then, the main elements for writing a specification for input to TuLiP are introduced. These include logic formulae, discrete transition systems annotated with predicates, and hybrid dynamical systems, with linear or piecewise affine continuous dynamics. The working principles of the algorithms for predicate abstraction and discrete game solving using nested fixpoints are explained, by following the input specification through the various transformations that compile it to a symbolic representation that scales well to solving large games. The tutorial concludes with several design examples that demonstrate the toolbox’s capabilities.  
Previous results in the use of pulsed air injection for active control of rotating stall have suggested that air injectors have the effect of shifting the steady state compressor characteristic. In this paper we analyze the effect of a compressor characteristic actuation scheme for the three state Moore Greitzer compression system model. It is shown that closed loop feedback based on the square magnitude of the first rotating stall mode can be used to decrease the hysteresis region associated with the transition from unstalled to stalled and back to unstalled operation. The compressor characteristic shifting idea is then applied to a higher fidelity distributed model in which the characteristic shifting has phase content in addition to the magnitude content captured by the three state model. The optimal phasing of the air injection relative to the sensed position of the stall cell is determined via simulation and the results found to agree with those obtained via an experimental parametric study on the Caltech low-speed axial flow compressor.}  +
As studies continue to demonstrate how our health is related to the status of our various commensal microbiomes, synthetic biologists are developing tools and approaches to control these microbiomes and stabilize healthy states or remediate unhealthy ones. Building on previous work to control bacterial communities, we have constructed a synthetic two-member bacterial consortium engineered to reach population density and composition steady states set by inducer inputs. We detail a screening strategy to search functional parameter space in this high-complexity genetic circuit as well as initial testing of a functional two-member circuit. We demonstrate non-independent changes in total population density and composition steady states with a limited set of varying inducer concentrations. After a dilution to perturb the system from its steady state, density and composition steady states are not regained. Modeling and simulation suggest a need for increased degradation of intercellular signals to improve circuit performance. Future experiments will implement increased signal degradation and investigate the robustness of control of each characteristic to perturbations from steady states.  +
This paper focuses on a new geometric approach to fully actuated control systems on the Riemannian manifold S^2. Our control laws exploit the basic and intuitive notions of geodesic direction and of distance between points, and generalize the classical proportional plus derivative feedback (PD) without the need of arbitrary local coordinate charts. Even for the stability analysis, the appropriate Lyapunov function relies upon the notion of distance and its properties. This methodology then applies to spin-axis stabilization of a spacecraft actuated by only two control torques: discarding the rotation about the unactuated axis, a reduced system is considered, whose state is in fact defined on the sphere. For this reduced attitude stabilization problem our approach allows us not only to deal optimally with the inevitable singularity, but also to achieve simplicity, versatility and (coordinate independent) adaptive capabilities.  +
Receding horizon control allows a blending of navigation and control functions at the inner and outer loop levels and significantly enhances the ability of the control system to react to complex dynamic and environmental constraints. In this paper, we explore some of the limits of receding horizon control, including the extent to which traditional control specifications can be cast as RHC problem specifications. Simulation results for a planar flight vehicle with representative flight dynamics illustrate the main features of the proposed approach.  +
This paper describes the use of time-delayed feedback to regulate the behavior of biological networks. The general ideas are demonstrated on specific transcriptional regulatory and neural networks. It is shown that robust yet tunable controllers can be constructed that provide the biological systems with model-engineered inputs. The results indicate that time delay modulation may serve as an efficient bio-compatible control tool.  +
Convergence properties of distributed consensus protocols on networks of dynamical agents have been analyzed by combinations of algebraic graph theory and control theory tools under certain assumptions, such as strong connectivity. Strong connectivity can be regarded as the requirement that the information of each agent propagates to all the others, possibly with intermediate steps and manipulations. However, because of network failures or malicious attacks, it is possible that this assumption no longer holds, so that some agents are only receiving or only transmitting information from other subsets of agents. In this case, strong connectivity is replaced by weak connectivity. We analyze the convergence properties of distributed consensus on directed graphs with weakly connected components. We show conditions for which the agreement is reached, and, for the cases in which such conditions do not hold, we provide bounds on the residual disagreement. in terms of the number of agents that must fail for the  +
Fault tolerance and safety verification of control systems are essential for the success of autonomous robotic systems. A control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, takes a goal-based control approach. In this paper, a method for converting goal network control programs into linear hybrid systems is developed. The linear hybrid system can then be verified for safety in the presence of failures using existing symbolic model checkers. An example task is developed and successfully verified using HyTech, a symbolic model checking software for linear hybrid systems.  +
The main result of this paper is a theorem that allows smooth, time-varying controllers which asymptotically stabilize a driftless nonlinear system to be converted to homogeneous, time-varying controllers which provide {\em exponential} stability. The resulting controllers are smooth everywhere except the origin and are easily computed given the original asymptotic stabilizer. We illustrate the result with experimental results on a simple mobile robot.  +
Optimal uncertainty quantification (OUQ) is a framework for nu- merical extreme-case analysis of stochastic systems with imperfect knowl- edge of the underlying probability distribution and functions/events. This paper presents sufficient conditions (when underlying functions are known) under which an OUQ problem can be reformulated as a finite-dimensional convex optimization problem.  +
How does one evaluate the performance of a stochastic system in the absence of a perfect model (i.e. probability distribution)? We address this question under the framework of optimal uncertainty quantification (OUQ), which is an information-based approach for worst-case analysis of stochastic systems. We are able to generalize previous results and show that the OUQ problem can be solved using convex optimization when the function under evaluation can be expressed in a polytopic canonical form (PCF). We also propose iterative methods for scaling the convex formulation to larger systems. As an application, we study the problem of storage placement in power grids with renewable generation. Numerical simulation results for simple artificial examples as well as an example using the IEEE 14-bus test case with real wind generation data are presented to demonstrate the usage of OUQ analysis.  +
Designing synthetic microbial consortia is an emerging area in synthetic biology and a major goal is to realize stable and robust coexistence of multiple species. Cooperation and competition are fundamental intra/interspecies interactions that shape population level behaviors, yet it is not well-understood how these interactions affect the stability and robustness of coexistence. In this paper, we show that communities with cooperative interactions are more robust to population disturbance, e.g., depletion by antibiotics, by forming intermixed spatial patterns. Meanwhile, competition leads to population spatial heterogeneity and more fragile coexistence in communities. Using reaction-diffusion and nonlocal PDE models and simulations of a two-species E. coli consortium, we demonstrate that cooperation is more beneficial than competition in maintaining coexistence in spatially structured consortia, but not in well-mixed environments. This also suggests a trade-off between constructing heterogeneous communities with localized functions and maintaining robust coexistence. The results provide general strategies for engineering spatially structured consortia by designing interspecies interactions and suggest the importance of cooperation for biodiversity in microbial community.  +
We introduce a class of triangulated graphs for algebraic representation of formations that allows us to specify a mission cost for a group of vehicles. This representation plus the navigational information allows us to formally specify and solve tracking problems for groups of vehicles in formations using an optimization-based approach. The approach is illustrated using a collection of six underactuated vehicles that track a desired trajectory in formation.<br>  +
This paper discusses a design methodology of cooperative trajectory generation for multi-robot systems. The trajectory of achieving cooperative tasks, i.e., with temporal constraints, is constructed by a nonlinear trajectory generation (NTG) algorithm. Three scenarios of multi-robot tasking are proposed at the cooperative task planning framework. The NTG algorithm is, then, used to generate real-time trajectory for desired robot activities. Given robot dynamics and constraints, the NTG algorithm first finds trajectory curves in a lower dimensional space and, then, parameterizes the curves by a set of B-spline representations. The coe�cients of the B-splines are further solved by the sequential quadratic programming to satisfy the optimization objectives and constraints. The NTG algorithm has been implemented to generate real-time trajectories for a group of cooperative robots in the presence of spatial and temporal constraints. Finally, an illustrated example of cooperative task planning with temporal constraints is presented.  +
There is a growing interest in building autonomous systems that interact with complex environments. The difficulty associated with obtaining an accurate model for such environments poses a challenge to the task of assessing and guaranteeing the system’s performance. We present a data-driven solution that allows for a system to be evaluated for specification conformance without an accurate model of the environment. Our approach involves learning a conservative reactive bound of the environment’s behavior using data and specification of the system’s desired behavior. First, the approach begins by learning a conservative reactive bound on the environment’s actions that captures its possible behaviors with high probability. This bound is then used to assist verification, and if the verification fails under this bound, the algorithm returns counter-examples to show how failure occurs and then uses these to refine the bound. We demonstrate the applicability of the approach through two case-studies: i) verifying controllers for a toy multi-robot system, and ii) verifying an instance of human-robot interaction during a lane-change maneuver given real-world human driving data.  +
This paper presents a method for optimal trajectory generation for discrete-time nonlinear systems with linear temporal logic (LTL) task specifications. Our approach is based on recent advances in stochastic optimization algorithms for optimal trajectory generation. These methods rely on estimation of the rare event of sampling optimal trajectories, which is achieved by incrementally improving a sampling distribution so as to minimize the cross-entropy. A key component of these stochastic optimization algorithms is determining whether or not a trajectory is collision-free. We generalize this collision checking to e�ciently verify whether or not a trajectory satisfies a LTL formula. Interestingly, this verification can be done in time polynomial in the length of the LTL formula and the trajectory. We also propose a method for e�ciently re-using parts of trajectories that only partially satisfy the specification, instead of simply discarding the entire sample. Our approach is demonstrated through numerical experiments involving Dubins car and a generic point-mass model subject to complex temporal logic task specifications.  +
D
In this paper, we consider the following problem. Suppose a sensor is taking measurements of a dynamic process. It needs to communicate the information over a network of communication links that can drop packets stochastically. What is the optimal processing at each node in the network? We provide a strategy that yields the optimal performance at the cost of constant memory and processing at each node. We also provide conditions on the network for the estimate error covariance to be stable under this algorithm.  +
We consider the problem of controlling a linear time invariant process when the controller is located at a location remote from where the sensor measurements are being generated. The communication from the sensor to the controller is supported by a communication network with arbitrary topology composed of analog erasure channels. Using a separation principle, we prove that the optimal LQG controller consists of an LQ optimal regulator along with an estimator that estimates the state of the process across the communication network mentioned above. We then determine the optimal information processing strategy that should be followed by each node in the network so that the estimator is able to compute the best possible estimate in the minimum mean squared error sense. The algorithm is optimal for any packet-dropping process and at every time step, even though it is recursive and hence requires a constant amount of memory, processing and transmission at every node in the network per time step. For the case when the packet drop processes are memoryless and independent across links, we analyze the stability properties and the performance of the closed loop system. The algorithm is an attempt to escape the more commonly used viewpoint of treating a network of communication links as a single end-to-end link with the probability of successful transmission determined by some measure of the reliability of the network.  +
This paper considers a group of agents that aim to reach an agreement on individually measured time-varying signals by local communication. In contrast to static network averaging problem, the consensus we mean in this paper is reached in a dynamic sense. A discrete-time dynamic average consensus protocol can be designed to allow all the agents tracking the average of their reference inputs asymptotically. We propose a minimal-time dynamic consensus algorithm, which only utilises minimal number of local observations of randomly picked node in a network to compute the final consensus signal. Our results illustrate that with memory and computational ability, the running time of distributed averaging algorithms can be indeed improved dramatically using local information as suggested by Olshevsky and Tsitsiklis.  +
We study a distributed multi-agent optimization problem of minimizing the sum of convex objective functions. A new decentralized optimization algorithm is introduced, based on dual decomposition, together with the subgradient method for finding the optimal solution. The iterative algorithm is implemented on a multi-hop network and is designed to handle communication delays. The convergence of the algorithm is proved for communication networks with bounded delays. An explicit bound, which depends on the communication delays, on the convergence rate is given. A numerical comparison with a decentralized primal algorithm shows that the dual algorithm converges faster, with less communication.  +
Temporal logic based synthesis approaches are often used to find trajectories that are correct-by-construction in systems–eg. synchronization for multi-agent hybrid systems, reactive motion planning for robots. However, the scalability of such approaches is of concern and at times a bottleneck when transitioning from theory to practice. In this paper, we identify a class of problems in the GR(1) fragment of linear-time temporal logic (LTL) where the synthesis problem allows for a decomposition that enables easy parallelization. This decomposition also reduces the alternation depth, resulting in more efficient synthesis. A multi-agent robot gridworld example with coordination tasks is presented to demonstrate the application of the developed ideas and also to perform empirical analysis for benchmarking the decomposition-based synthesis approach.  +
Using tools from dynamical systems and systems identification we develop a framework for the study of primitives for human motion, which we refer to as movemes. The objective is understanding human motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet of dynamical systems. In this work we address the problem of defining conditions under which collections of signals are well-posed according to a dynamical model class M and then can generate movemes. Based on the assumption of well-posedness, we develop segmentation and classification algorithms in order to reduce a complex activity into the sequence of movemes that have generated it. Using examples we show that the definition of well-posedness can be applied in practice and show analytically that the proposed algorithms are robust with respect to noise and model uncertainty. We test our ideas on data sampled from five human subjects who were drawing figures using a computer mouse. Our experiments show that we are able to distinguish between movemes and recognize them even when they take place in activities containing more than one moveme at a time.  +
In this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection. With the geometric insight gained with this decomposition, we are able to easily prove some special results for this class of control systems. Examples illustrate the theory.  +
In this paper we explore the use of time-delayed differential equation as a means of obtaining a simplified description of very high order dynamics.This paper finds results for a particular type of system, a single-input single-output (SISO) linear system with a nonlinear feedback. We begin with a high dimensional system in state space and reduce the dimension by finding a delay based approximation which could be a smaller set of integro-differential equations or DDEs. We argue that approximations of high order linear subsystems whose distribution functions have relatively smaller variance such as delta functions, give a conservative approximation of a system's stable parameter space. Through examples inspired by biology, we show how these approximations can be used to verify stability. We analyze the system's stability and robustness dependence on statistical properties, mainly relative variance and expectation for a symmetric distribution function.  +
Motivated by the availability of different types of delays in embedded systems and biological circuits, the objective of this work is to study the benefits that delay can provide in simplifying the implementation of controllers for continuous-time systems. Given a continuous-time linear time-invariant (LTI) controller, we propose three methods to approximate this controller arbitrarily precisely by a simple controller composed of delay blocks, a few integrators and possibly a unity feedback. Different problems associated with the approximation procedures, such as finding the optimal number of delay blocks or studying the robustness of the designed controller with respect to delay values, are then investigated. We also study the design of an LTI continuous-time controller satisfying given control objectives whose delay-based implementation needs the least number of delay blocks. A direct application of this work is in the sampled-data control of a real-time embedded system, where the sampling frequency is relatively high and/or the output of the system is sampled irregularly. Based on our results on delay-based controller design, we propose a digital-control scheme that can implement every continuous-time stabilizing (LTI) controller. Unlike a typical sampled-data controller, the hybrid controller introduced here---consisting of an ideal sampler, a digital controller, a number of modified second-order holds and possibly a unity feedback---is robust to sampling jitter and can operate at arbitrarily high sampling frequencies without requiring expensive, high-precision computation.  +
Genetic regulatory networks are biochemical reaction systems, consisting of a network of interacting genes and associated proteins. The dynamics of genetic regulatory networks contain many complex facets that require careful consideration during the modeling process. The classical modeling approach involves studying systems of ordinary differential equations (ODEs) that model biochemical reactions in a deterministic, continuous, and instantaneous fashion. In reality, the dynamics of these systems are stochastic, discrete, and widely delayed. The first two complications are often successfully addressed by modeling regulatory networks using the Gillespie stochastic simulation algorithm (SSA), while the delayed behavior of biochemical events such as transcription and translation are often ignored due to their mathematically difficult nature. We develop techniques based on delay-differential equations (DDEs) and the delayed Gillespie SSA to study the effects of delays, in both continuous deterministic and discrete stochastic settings. Our analysis applies techniques from Floquet theory and advanced numerical analysis within the context of delay-differential equations, and we are able to derive stability sensitivities for biochemical switches and oscillators across the constituent pathways, showing which pathways in the regulatory networks improve or worsen the stability of the system attractors. These delay sensitivities can be far from trivial, and we offer a computational framework validated across multiple levels of modeling fidelity. This work suggests that delays may play an important and previously overlooked role in providing robust dynamical behavior for certain genetic regulatory networks, and perhaps more importantly, may offer an accessible tuning parameter for robust bioengineering.  +
Integral control is commonly used in mechanical and electrical systems to ensure perfect adaptation. A proposed design of integral control for synthetic biological systems employs the sequestration of two biochemical controller species. The unbound amount of controller species captures the integral of the error between the current and the desired state of the system. However, implementing integral control inside bacterial cells using sequestration feedback has been challenging due to the controller molecules being degraded and diluted. Furthermore, integral control can only be achieved under stability conditions that not all sequestration feedback networks fulfill. In this work, we give guidelines for ensuring stability and good performance (small steady-state error) in sequestration feedback networks. Our guidelines provide simple tuning options to obtain a flexible and practical biological implementation of sequestration feedback control. Using tools and metrics from control theory, we pave the path for the systematic design of synthetic biological systems.  +
In this study, an Escherichia coli (E. coli) based transcription translation cell-free system (TX-TL) was employed to sample various enzyme expression levels of the violacein pathway. TX-TL enables rapid modifications and prototyping of the pathway without complicated cloning cycles. The violacein metabolic pathway has been successfully reconstructed in TX-TL. Analysis of the product via UV-Vis absorption and liquid chromatography-mass spectrometry detected 4.95 mM of violacein. Expression levels of pathway enzymes were modeled using the TX-TL Toolbox. The model revealed the length of an enzyme coding sequence (CDS) significantly affected its expression level. Finally, pathway exploration suggested an improvement in violacein production at high VioC and VioD DNA concentrations.  +
This paper describes the design, modeling, synthesis and preliminary validation of a protein concentration regulator circuit. The circuit is designed to maintain the level of a target protein to a reference level, specified by the amount of another protein. This is implemented using a single negative feedback loop that inhibited the production of the target protein once its concentration was equal to the reference amount. A mathematical model consisting of a set of ODEs is derived from mass action laws and Hill function approximations of protein production. Steady-state analysis of the model is used to predict parameter sensitivity and experimental behavior. We implemented this circuit in ''E. coli'' using scaffold-based sequestration and transcriptional activation. Preliminary experimental results show the system matching predictions from our model and performing the expected task.  +
Current bacterial synthetic circuits rely on the fast dilution and high protein expression that occurs during exponential phase. However, constant exponential phase is both difficult to ensure in a lab environment and almost certainly impractical in any natural setting. Here, we characterize the performance of 13 E. coli native 38 promoters, as well as a previously identified 38 consensus promoter. We then make tetO combinatorial versions of the three strongest promoters to allow for inducible delayed expression. The design of these combinatorial promoters allows for design of circuits with inducible stationary phase activity that can be used for phase-dependent delays in dynamic circuits or spatial partitioning of biofilms.  +
As a field, synthetic biology strives to engineer increasingly complex artificial systems in living cells. Active feedback in closed loop systems offers a dynamic and adaptive way to ensure constant relative activity independent of intrinsic and extrinsic noise. In this work, we use synthetic protein scaffolds as a modular and tunable mechanism for concentration tracking through negative feedback. Input to the circuit initiates scaffold production, leading to colocalization of a two-component system and resulting in the production of an inhibitory antiscaffold protein. Using a combination of modeling and experimental work, we show that the biomolecular concentration tracker circuit achieves dynamic protein concentration tracking in ''Escherichia coli'' and that steady state outputs can be tuned.  +
This paper proposes a new synthetic in vitro circuit that aims at regulating the rate of RNA transcription through positive feedback interactions. This design is dual to a previously synthesized transcriptional rate regulator based on self-repression. Two DNA templates are designed to interact through their transcripts, creating cross activating feedback loops that will equate their transcription rates at steady state. A mathematical model is developed for this circuit, consisting of a set of ODEs derived from the mass action laws and Michaelis--Menten kinetics involving all the present chemical species. This circuit is then compared to its regulatory counterpart based on negative feedback. A global sensitivity analysis reveals the fundamental features of the two designs, by evaluating their equilibrium response to changes in the most crucial parameters of the system.  +
RNA thermometers mediate responses to temperature changes in various natural circuits, and have been developed in a synthetic context as well. However, a toolbox of RNA thermometers with diâµerent sensitivities to temperature is lacking. Here, we address this issue using a combination of computational and experimental methodologies. We analysed a set of available synthetic RNA thermometers through a quantification of their activity as a function of temperatures in a cell- free expression molecular breadboard system as well as through computation of their melt profiles. Based on this, we computed melt profiles of a library of RNA thermometers and found that the library contained RNA thermometers with a range of sensitivities and thresholds in their response to temperature. We constructed this library and found, through preliminary measurements, a wide range of responses to temperature, which in some cases matched the computational predictions. The constructed library represents a toolbox of RNA thermometers with different sensitivities and is foun- dational work towards synthetic biology applications such as efficient control of large volume chemical reactors, precise spatiotemporal control of gene expression as well as tools to engineer robustness to temperature in biomolecular circuits.  +
Feedback control is the key to achieve robust performances for many engineered systems. However, its application in biological contexts is still largely unexplored. In this work, we designed, analyzed and simulated a layered controller functioning at both molecular and populational levels. First, we used a minimal model of three states to represent a system where state A activates state B; state R is a by-product of state B that acts as a negative feedback regulating both state A, B, and sequentially R. We call the feedback applied to state B a cis feedback and the one applied to state A a trans feedback. Through stability analysis via linearization at equilibrium and sensitivity analysis at transient state, we found that the cis feedback attenuates disturbances better but recovers slower; the trans feedback recovers faster but has more dramatic responses to fluctuations; the layered feedback demonstrates both advantageous traits of the two single layers. Then we designed two versions of synthetic genetic circuits to implement the layered controller in living cells. One version with an sRNA as regulator R, the other with a transcription factor protein as the regulator R. The analysis and dynamical simulation of the models confirmed the analytical results from the minimal model. At the same time, we found that the protein regulated feedback controls have faster recovery speed but the RNA version has a stronger disturbance attenuation effect.  +
This paper describes a synthetic in vitro genetic circuit programmed to work as an insulating device. This circuit is composed of nucleic acids, which can be designed to interact according to user defined rules, and of few proteins that perform catalytic functions. A model of the circuit is derived from first principle biochemical laws. This model is shown to exhibit time-scale separation that makes its output insensitive to downstream time varying loads. Simulation results show the circuit effectiveness and represent the starting point for future experimental testing of the device.  +
âIncoherent feedforward loopsâ represent important biomolecular circuit elements capable of a rich set of dynamic behavior including adaptation and pulsed responses. Temperature can modulate some of these properties through its effect on the underlying reaction rate parameters. It is generally unclear how to design a circuit where these properties are robust to variations in temperature. Here, we address this issue using a combination of tools from control and dynamical systems theory as well as preliminary experimental measurements towards such a design. Using a structured uncertainty representation, we analyze a standard incoherent feedforward loop circuit, noting mechanisms that intrinsically confer temperature robustness to some of its properties. Further, we study design variants that can enhance this robustness to temperature, including different negative feedback configurations as well as conditions for perfect temperature compensation. Finally, we find that the response of an incoherent feedforward loop circuit in cells can change with temperature. These results present groundwork for the design of a temperature-robust incoherent feedforward loop circuit.  +
In this paper we give a formulation of differential flatness---a concept originally introduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalence between exterior differential systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. The original definition of flatness was given in the context of differentiable algebra, and required that all mappings be meromorphic functions. Our formulation of flatness does not require any algebraic structure and allows one to use tools from exterior differential systems to help characterize differentially flat systems. In particular, we shown that in the case of single input control systems (i.e., codimension 2 Pfaffian systems), a system is differentially flat if and only if it is feedback linearizable via static state feedback. However, in higher codimensions feedback linearizability and flatness are *not* equivalent: one must be careful with the role of time as well the use of prolongations which may not be realizable as dynamic feedbacks in a control setting. Applications of differential flatness to nonlinear control systems and open questions will be discussed.  +
This paper describes the application of differential flatness techniques from nonlinear control theory to mechanical (Lagrangian) systems. Systems which are differentially flat have several useful properties which can be exploited to generate effective control strategies for nonlinear systems. For the special case of mechanical control systems, much more geometric information is present and the purpose of this paper is to explore the implications and features of that class of systems. We concentrate on several worked examples which illustrate the general theory and present a detailed catalog of known examples of differentially flat mechanical systems.  +
Given a differentially flat system of ODEs, flat outputs that depend only on original variables but not on their derivatives are called zero-flat outputs and systems possessing such outputs are called zero-flat. In this paper we present a theory of zero-flatness for a system of two one-forms in arbitrary number of variables $(t,x^1,\dots,x^N)$. Our approach splits the task of finding zero-flat outputs into two parts. First part involves solving for distributions that satisfy a set of algebraic conditions. If the first part has no solution then the system is not zero-flat. The second part involves finding an integrable distribution from the solution set of the first part. Typically this part involves solving PDEs. Our results are also applicable in determining if a control affine system in $n$ states and $n-2$ controls has flat outputs that depend only on states. We illustrate our method by examples.  +
Differentially flat systems are underdetermined systems of (nonlinear) ordinary differential equations (ODEs) whose solution curves are in smooth one-one correspondence with arbitrary curves in a space whose dimension equals the number of equations by which the system is underdetermined. For control systems this is the same as the number of inputs. The components of the map from the system space to the smaller dimensional space are referred to as the flat outputs. Flatness allows one to systematically generate feasible trajectories in a relatively simple way. Typically the flat outputs may depend on the original independent and dependent variables in terms of which the ODEs are written as well as finitely many derivatives of the dependent variables. Flatness of systems underdetermined by one equation is completely characterised by Elie Cartan's work. But for general underdetermined systems no complete characterisation of flatness exists. <p> In this dissertation we describe two different geometric frameworks for studying flatness and provide constructive methods for deciding the flatness of certain classes of nonlinear systems and for finding these flat outputs if they exist. We first introduce the concept of ``absolute equivalence'' due to Cartan and define flatness in this frame work. We provide a method of testing for the flatness of systems, which involves making a guess for all but one of the flat outputs after which the problem is reduced to the case solved by Cartan. Secondly we present an alternative geometric approach to flatness which uses ``jet bundles'' and present a theorem which partially characterises flat outputs that depend only on the original variables but not on their derivatives, for the case of systems described by two independent one-forms in arbitrary number of variables. Finally, for the class of Lagrangian mechanical systems whose number of control inputs is one less than the number of degrees of freedom, we provide a characterisation of flat outputs that depend only on the configuration variables, but not on their derivatives. This characterisation makes use of the Riemannian metric provided by the kinetic energy of the system.  
This paper proposes a real-time planning scheme and its implementation for a class of dynamic systems. The planner is aimed to satisfy the state equations, the path and actuator constriants, and the given initial and terminal constraints. In order to generate trajectories in real-time, three broad steps are performed: (1) the structure of differentially flat systems is used to explicitly encapsulate the state equations into linear differential constraints in a flat space, and appropriately transform the boundary conditions; (ii) using semi-infinite optimization theory, an inner approximation of nonlinear constraints is made to replace these by a set of linear inequalities in the flat space, i.e., by a polytope; (iii) this polytopic representation of the system that satisfies the state equations and the constraints is then parameterized using basis functions and the planning problem is turned around into solution of a set of linear inequalities in the coefficient space of the basis functions. It is then demonstrated that numerically efficient algorithms can be built to solve the planning problem in real-time. The essence of the approach is demonstrated by two examples: (1) an implementation is performed on a spring-mass-damper system to demonstrate the real-time capability of evasion-pursuit; (ii) a VTOL aircraft is used to illustrate the application of this approach in simulation to nonlinear problems.  +
We describe a method for discrete representation of continuous functions and show how this may be used for typical computations in nonlinear control desi gn. The method involves representing functions by their values and finitely many derivatives at discrete set of points on the domain. We propose a grid structure based on a hierarchy of rectangular boxes that provides flexibility in placing grid points densely in some regions and sparsely in the other. The grids possess enough structure to facilitate easy interpolation schemes based on piecewise polynomials. We illustrate the method using a simple example where we compute the feedback linearizing output of a system.  +
We address the problem of estimating discrete variables in a class of deterministic transition systems where the continuous variables are available for measurement. This simplified scenario has practical interest, for example, in the case of decentralized multi-robot systems. In these systems, the continuous variables represent physical quantities such as the position and velocity of a robot, while discrete variables may represent the state of the logical system that is used for control and coordination. We propose a novel approach to the estimation of discrete variables using basic lattice theory that overcomes some of the severe complexity issues encountered in previous work. We show how to construct the proposed estimator for a multi-robot system performing a cooperative assignment task.  +
The problem of estimating the discrete variables in nondeterministic hybrid systems where the continuous variables are available for measurement is considered. Using partial order and lattice theory, we construct a discrete state estimator, the LU estimator, which updates two variables at each step. Namely, it updates the lower (L) and upper (U) bounds of the set of all possible discrete variables values compatible with the output sequence and with the systems' dynamics. If the system is weakly observable, we show that there always exist a lattice on which to construct the LU estimator. For computational issues, some partial orders are to be preferred to others.We thus show that nondeterminism may be added to a system so as to obtain a new system that satisfies the requirements for the construction of the LU estimator on a chosen lattice. These ideas are applied to a nondeterministic multi-robot system.  +
Distributed algorithms for averaging have at- tracted interest in the control and sensing literature. However, previous works have not addressed some practical concerns that will arise in actual implementations on packet-switched communication networks such as the Internet. In this paper, we present several implementable algorithms that are robust to asynchronism and dynamic topology changes. The algorithms do not require global coordination and can be proven to converge under very general asynchronous timing assumptions. Our results are verified by both simulation and experiments on a real-world TCP/IP network.  +
A cooperative control system consists of multiple, autonomous components interacting to<br> control their environment. Examples include air tra±c control systems, automated factories,<br> robot soccer teams and sensor/actuator networks. Designing such systems requires a combination of tools from control theory and distributed systems. In this article, we review some of these tools and then focus on the Computation and Control Language, CCL, which we have developed as a modeling tool and a programming language for cooperative control systems.  +
In this paper, we propose a framework for formation stabilization of multiple autonomous vehicles in a distributed fashion. Each vehicle is assumed to have simple dynamics, i.e. a double-integrator, with a directed (or an undirected) information ow over the formation graph of the vehicles. Our goal is to find a distributed control law (with an efficient computational cost) for each vehicle that makes use of limited information regarding the state of other vehicles. Here, the key idea in formation stabilization is the use of natural potential functions obtained from structural constraints of a desired formation in a way that leads to a collision-free, distributed, and bounded state feedback law for each vehicle.  +
Many systems comprised of interconnected sub-units exhibit coordinated behaviors; social groups, networked computers, financial markets, and numerous biological systems come to mind. There has been long-standing interest in developing a scientific understanding of coordination, both for ex- planatory power in the natural and economic sciences, and also for constructive power in engineering and applied sciences. This thesis is an abstract study of coordination, focused on developing a sys- tematic âdesign theoryâ for producing interconnected systems with specifiable coordinated behavior; this is in contrast to the bulk of previous work on this sub ject, in which any design component has been primarily ad-hoc. <p>The main theoretical contribution of this work is a geometric formalism in which to cast dis- tributed systems. This has numerous advantages and ânaturallyâ parametrizes a wide class of distributed interaction mechanisms in a uniform way. We make use of this framework to present a model for distributed optimization, and we introduce the distributed gradient as a general design tool for synthesizing dynamics for distributed systems. The distributed optimization model is a useful abstraction in its own right and motivates a definition for a distributed extremum. As one might expect, the distributed gradient is zero at a distributed extremum, and the dynamics of a distributed gradient flow must converge to a distributed extremum. This forms the basis for a wide variety of designs, and we are in fact able to recover a widely studied distributed averaging algorithm as a very special case. <p>We also make use of our geometric model to introduce the notion of coordination capacity; intuitively, this is an upper bound on the âcomplexityâ of coordination that is feasible given a particular distributed interaction structure. This gives intuitive results for local, distributed, and global control architectures, and allows formal statements to be made regarding the possibility of âsolvingâ certain optimization problems under a particular distributed interaction model. <p>Finally, we present a number of applications to illustrate the theoretical approach presented; these range from âstandardâ distributed systems tasks (leader election and clock synchronization) to more exotic tasks like graph coloring, distributed account balancing, and distributed statistical computations.  
We present an approach that allows mission and contingency management to be achieved in a distributed and dynamic manner without any central control over multiple software modules. This approach comprises two key elements---a mission management subsystem and a Canonical Software Architecture (CSA) for a planning subsystem. The mission management subsystem works in conjunction with the planning subsystem to dynamically replan in reaction to contingencies. The CSA ensures the consistency of the states of all the software modules in the planning subsystem. System faults are identified and replanning strategies are performed distributedly in the planning and the mission management subsystems through the CSA. The approach has been implemented and tested on Alice, an autonomous vehicle developed by the California Institute of Technology for the 2007 DARPA Urban Challenge.  +
We consider the problem of designing distributed control protocols -for aircraft vehicle management systems- that cooperatively allocate electric power while meeting certain higher level goals and requirements, and dynamically reacting to the changes in the internal system state and external environment. A decentralized control problem is posed where each power distribution unit is equipped with a controller that implements a local protocol to allocate power to a certain subset of loads. We use linear temporal logic as the specification language for describing correct behaviors of the system (e.g., safe operating conditions) as well as the admissible dynamic behavior of the environment due to, for example, wind gusts and changes in system health. We start with a global specification and decompose it into local ones. These decompositions allow the protocols for each local controller to be separately synthe- sized and locally implemented while guaranteeing the global specifications to hold. Through a design example, we show that by refining the interface rules between power distribution units, it is possible to reduce the total power requirement.  +
We consider the control of interacting subsystems whose dynamics and constraints are uncoupled, but whose state vectors are coupled non-separably in a single centralized cost function of a finite horizon optimal control problem. For a given centralized cost structure, we generate distributed optimal control problems for each subsystem and establish that the distributed receding horizon implementation is asymptotically stabilizing. The communication requirements between subsystems with coupling in the cost function are that each subsystem obtain the previous optimal control trajectory of those subsystems at each receding horizon update. The key requirements for stability are that each distributed optimal control not deviate too far from the previous optimal control, and that the receding horizon updates happen sufficiently fast. The theory is applied in simulation for stabilization of a formation of vehicles.  +
This work is an extension to a companion paper describing consensus-tracking for networked agents, and shows how those results can be applied to obtain least-squares fused estimates based on spatially distributed measurements. This mechanism is very robust to changes in the underlying network topology and performance, making it an interesting candidate for sensor fusion on autonomous mobile networks. We conclude with an example of a preliminary application to distributed Kalman Filtering using the proposed technique, illustrating the dependence of the performance on the structure of the underlying network.  +
In this paper, we provide a theoretical framework that consists of graph theoretical and Lyapunov-based approaches to stability analysis and distributed control of multi-agent formations. This framework relays on the notion of graph rigidity as a means of identifying the shape variables of a formation. Using this approach, we can formally define formations of multiple vehicles and three types of stabilization/tracking problems for dynamic multi-agent systems. We show how these three problems can be addressed mutually independent of each other for a formation of two agents. Then, we introduce a procedure called dynamic node augmentation that allows construction of a larger formation with more agents that can be rendered structurally stable in a distributed manner from some initial formation that is structurally stable. We provide two examples of formations that can be controlled using this approach, namely, the V-formation and the diamond formation.  +
We consider the problem of synthesizing control protocols for smart camera networks where the goal is to guarantee that certain linear temporal logic (LTL) specifications related to a given surveillance task are met. We first present a centralized control architecture for assigning pan-tilt-zoom (PTZ) cameras to targets so that the specification is met for any admissible behavior of the targets. Then, in order to alleviate the computational complexity associated with LTL synthesis and to enable implementation of local control protocols on individual PTZ cameras, we propose a distributed synthe- sis methodology. The main idea is to decompose the global specification into local specifications for each PTZ camera. A thorough design example is presented to illustrate the steps of the proposed procedure.  +
This work examines several dynamical aspects of average consensus in mobile networks. The results herein allow consensus on general time-varying signals, and allow tracking analysis using standard frequency-domain techniques. Further, the frequency-domain analysis naturally inspires a robust small-gain version of the algorithm, which tolerates arbitrary non-uniform time delays. Finally, we show how to exploit a dynamical conservation property in order to ensure consensus tracking despite splitting and merging of the underlying mobile network.  +
This paper presents an experimental investigation into the effect of a varying downstream boundary condition on dynamic separation control in a twodimensional low-speed asymmetric diffuser. The potential for coupling between the downstream boundary condition and the separation dynamics is relevant, for example, in using separation control to enable more aggressive serpentine aircraft inlets, where the compressor may be close to the separation point. Separation control in the experiment is obtained using spanwise unsteady forcing from a single tangential actuator located directly upstream of the separation point. The downstream boundary condition simulates the dominant quasi-steady and reflection characteristics of a compressor. Although the boundary condition affects the uncontrolled pressure recovery, the optimal forcing frequency is shown to depend only on the mass flow rate and not on either the presence, impedance, or location of the downstream boundary condition. At the conditions tested herein, we therefore conclude that the mechanism underlying dynamic separation control is local in nature, and is not influenced by global system dynamics.  +
We consider the problem of estimating the discrete state of an aircraft electric system under a distributed control architecture through active sensing. The main idea is to use a set of controllable switches to reconfigure the system in order to gather more information about the unknown state. By adaptively making a sequence of reconfiguration decisions with uncertain outcome and by correlating the measurements and prior information to make the next decision, we aim to reduce the uncertainty. A greedy strategy is developed that maximizes the one-step expected uncertainty reduction. By exploiting recent results on adaptive submodularity, we give theoretical guarantees on the worst-case performance of the greedy strategy. We apply the proposed method in a fault de- tection scenario where the discrete state captures possible faults in various circuit components. In addition, simple abstraction rules are proposed to alleviate state space explosion and to scale up the strategy. Finally, the efficiency of the proposed method is demonstrated empirically on different circuits.  +
We investigate nonlinear dynamical models for self- sustained oscillations in the flow past a rectangular cavity. The models are based on the method of Proper Orthogonal Decomposition (POD) and Galerkin projection, and we introduce an inner product and formulation of the equations of motion which enables one to use vector-valued POD modes for compressible flows. We obtain models between 3 and 20 states, which accurately describe both the short-time and long-time dynamics. This is a substantial improvement over previous models based on scalar-valued POD modes,which capture the dynamics for short time, but deviate for long time.  +
Locomotion of microorganisms and tiny artificial swimmers is governed by low- Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer's trajectories, and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a micro-swimmer near a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying geometric structure of the dynamics, and establish a relation between the reversing symmetry of the system and existence and stability of periodic and steady solutions of motion near the wall. The results are demonstrated by numerical simulations and validated by motion experiments with robotic swimmer prototypes.  +
We study the dynamic stability of low Reynolds number swimming near a plane wall from a control-theoretic viewpoint. We consider a special class of swimmers having a constant shape, focus on steady motion parallel to the wall, and derive conditions under which it is passively stable without sensing or feedback. We study the geometric structure of the swimming equation and highlight the relation between stability and reversing symmetry of the dynamical system. Finally, our numerical simulations reveal the existence of stable periodic motion. The results have implications for design of miniature robotic swimmers, as well as for explaining the attraction of micro-organisms to surfaces.  +
E
In mobile sensor networks, sensor measurements as well as control commands are transmitted over wireless time-varying links. It then becomes considerably important to address the impact of imperfect communication on the overall performance. In this paper, we study the effect of time-varying communication links on the control performance of a mobile sensor node. In particular, we investigate the impact of fading. We derive key performance measure parameters to evaluate the overall feedback control performance over narrowband channels. We show that fading can result in considerable delay and/or poor performance of the mobile sensor depending on the system requirements. To improve the performance, we then show how the application layer can use the channel status information of the physical layer to adapt control commands accordingly. We show that sharing information across layers can improve the overall performance considerably. We verify our analytical results by simulating a wireless speed control problem.  +
AbstractâIn this paper, we consider a state estimation problem over a bandwidth limited network. A sensor network consisting of N sensors is used to observe the states of M plants, but only p · N sensors can transmit their measurements to a centralized estimator at each time. Therefore a suitable scheme that schedules the proper sensors to access the network at each time so that the total estimation error is minimized is required. We propose four different sensor scheduling schemes. The static and stochastic schemes assume no feedback from the estimator to the scheduler, while the two dynamic schemes, Maximum Error First (MEF) and Maximum Deduction First (MDF) assume such feedback is available. We compare the four schemes via some examples and show MEF and MDF schemes are better than the static and stochastic schemes, which demonstrates that feedback can play an important role in this remote state estimation problem. We also show that MDF is better than MEF as MDF considers the total estimation error while MEF considers the individual estimation error.  +
In this paper, we consider a state estimation problem over a bandwidth limited network. A sensor network consisting of N sensors is used to observe the states of M plants, but only p les N sensors can transmit their measurements to a centralized esti.....  +
Thin film deposition is an industrially-important process that is highly dependent on the process conditions. Most films are grown under constant conditions, but a few studies show that modified properties may be obtained with periodic inputs. However, assessing the effects of modulation experimentally becomes impractical with increasing material complexity. Here we consider periodic conditions in which the period is short relative to the time-scales of growth. We analyze a stochastic model of thin film growth, computing effective transition rates associated with rapid periodic process parameters. Combinations of effective rates may exist which are not attainable under steady conditions, potentially enabling new film properties. An algorithm is presented to construct the periodic input for a desired set of effective transition rates. These ideas are first illustrated by two simple examples using kinetic Monte Carlo simulations and are then compared to existing deposition techniques.  +
Bifurcations are ubiquitous in engineering applications. Subcritical bifurcations are typically associated with hysteresis and catastrophic instability inception, while supercritical bifurcations are usually associated with gradual and more benign instability inception. With the assumption that the bifurcating modes are linearly unstabilizable, we give a constructive procedure of designing feedback laws to change the criticality of bifurcations from subcritical to supercritical. Algebraic necessary and sufficient conditions are obtained under which the criticality of a simple steady-state or Hopf bifurcation can be changed to supercritical by a smooth feedback. The effects of magnitude saturation, bandwidth, and rate limits are important issues in control engineering. We give qualitative estimates of the region of attraction to the stabilized bifurcating equilibrium/periodic orbits under these constraints. <p> We apply the above theoretical results to the Moore-Greitzer model in active control of rotating stall and surge in gas turbine engines. Though linear stabilizability can be achieved using distributed actuation, it limits the practical usefulness due to considerations of affordability and reliability. On the other hand, simple but practically promising actuation schemes such as outlet bleed valves, a couple of air injectors, and magnetic bearings will make the system loss of linear stabilizability, thus the control design becomes a challenging task. The above mentioned theory in bifurcation stabilization can be applied to these cases. We analyze the effects of magnitude and rate saturations in active control of rotating stall using bleed valves. Analytic formulas are obtained for the operability enhancement as a function of system parameters, noise level, and actuator magnitude and rate limits. The formulas give good qualitative predictions when compared with experiments. Our conclusion is that actuator magnitude and rate limits are serious limiting factors in stall control and must be addressed in practical implementation to the aircraft engines. <p>  
Motivated by problems such as active control of rotating stall in compression systems, an analysis of the effects of controller magnitude saturation in feedback stabilization of steady-state bifurcations is performed. In particular the region of attraction to the stabilized bifurcated equilibria is solved for feedback controllers with magnitude saturation limits using the technique of center manifold reduction and bifurcation analysis. It has been shown that the stability boundary is the saturation envelope formed by the unstable (or stable) equilibria for the closed loop system when the controllers saturate. The framework allows the design of feedback control laws to achieve desirable size of region of attraction when the noise is modeled as a closed set of initial conditions in the phase space. It is also possible to extend the techniques and results to Hopf bifurcations.  +
Operability enhancement is one of the major goals for active control of rotating stall and surge in aeroengines. The model developed by Moore and Greitzer exhibits the qualitative behavior of rotating stall and surge dynamics and thus can be used for controller designs. Based on this model, we derive a normal form from which explicit relations between the stall and surge inception process and the shape of compressor characteristics are obtained via bifurcation analysis. Analysis for the normal form with bleed valve actuator dynamics shows that under certain circumstances the optimal control is the "bang-on" control law that drives the bleed valve to open against its rate limit once the disturbances grow out of the noise level.  +
In this paper we analyze the effects of fluid noise, actuator bandwidth, magnitude saturation and rate limits on rotating stall control by studying a two dimensional system which is the approximation of the dynamics on the attracting saddle-sink connections of the three state low $B$ parameter Moore Greitzer model together with the dynamics of the bleed valve controller. We show that the region of attraction to the stabilized rotating stall equilibria is seriously restrained by the fluid noise level, the actuator bandwidth, magnitude saturation and rate limits. The bandwidth and rate requirement for a fixed extension of stable region is estimated by calculating the stable manifold of the saddle fixed point of the two dimensional system.  +
ugmented finite transition systems generalize nondeterministic transition systems with additional liveness conditions. We propose efficient algorithms for synthesizing control protocols for augmented finite transition systems to satisfy high-level specifications expressed in a fragment of linear temporal logic (LTL). We then use these algorithms within a framework for switching protocol synthesis for discrete-time dynamical systems, where augmented finite transition systems are used for abstracting the underlying dynamics. We introduce a notion of minimality for abstractions of certain fidelity and show that such minimal abstractions can be exactly computed for switched affine systems. Additionally, based on this framework, we present a procedure for computing digitally implementable switching protocols for continuous-time systems. The effectiveness of the proposed framework is illustrated through two examples of temperature control for buildings.  +
Motivated by robotic motion planning, we develop a framework for control policy synthesis for both non-deterministic transition systems and Markov decision processes that are subject to temporal logic task specifications. We introduce a fragment of linear temporal logic that can be used to specify common motion planning tasks such as safe navigation, response to the environment, surveillance, and persistent coverage. This fragment is computationally efficient; the complexity of control policy synthesis is a doubly-exponential improvement over standard linear temporal logic for both non-deterministic transition systems and Markov decision processes. This improvement is possible since we compute directly on the original system, as opposed to the automata-based approach commonly used for linear temporal logic. We give simulation results for representative motion planning tasks and compare to generalized reactivity(1).  +
In this paper we use ellipsoidal cones to achieve rendezvous of multiple agents. Rendezvous of multiple agents is shown to be equivalent to ellipsoidal cone invariance and a controller synthesis framework is presented. We first demonstrate the methodology on first order LTI systems and then extend it to rendezvous of mechanical systems, that is systems that are force driven.  +
Reinforcement Learning (RL) algorithms have found limited success beyond simulated applications, and one main reason is the absence of safety guarantees during the learning process. Real world systems would realistically fail or break be- fore an optimal controller can be learned. To address this issue, we propose a controller architecture that combines (1) a model-free RL-based controller with (2) model-based controllers utilizing control barrier functions (CBFs) and (3) on- line learning of the unknown system dynamics, in order to ensure safety during learning. Our general framework lever- ages the success of RL algorithms to learn high-performance controllers, while the CBF-based controllers both guarantee safety and guide the learning process by constraining the set of explorable polices. We utilize Gaussian Processes (GPs) to model the system dynamics and its uncertainties. Our novel controller synthesis algorithm, RL-CBF, guaran- tees safety with high probability during the learning process, regardless of the RL algorithm used, and demonstrates greater policy exploration efficiency. We test our algorithm on (1) control of an inverted pendulum and (2) autonomous car-following with wireless vehicle-to-vehicle communication, and show that our algorithm attains much greater sample efficiency in learning than other state-of-the-art algorithms and maintains safety during the entire learning process.  +
The mammalian gut contains trillions of microbes that interact with host cells and monitor changes in the environment. Opportunistic pathogens exploit environmental conditions to stimulate their growth and virulence, leading to a resurgence of chronic disorders such as inflammatory bowel disease (IBD). Current therapies are effective in less than 30% of patients due to the lack of adherence to prescription schedules and overall, off-target effects. Smart microbial therapeutics can be engineered to colonize the gut, providing in situ surveillance and conditional disease modulation. However, many current engineered microbes can only respond to single gut environmental factors, limiting their effectiveness. In this work, we implement the previously characterized split activator AND logic gate in the probiotic E. coli strain Nissle 1917. Our system can respond to two input signals: the inflammatory biomarker tetrathionate and a second input signal, IPTG. We report 4-6 fold induction with minimal leak when both signals are present. We model the dynamics of the AND gate using chemical reaction networks, and by tuning parameters in silico, we identified perturbations that affect our circuit's selectivity. We anticipate that our results will prove useful for designing living therapeutics for spatial targeting and signal processing in complex environments.  +
In this paper, we analyze the oscillatory dynamics of a class of cyclic gene regulatory networks and provide engineering principles for the robust synthesis of biochemical oscillators. We first review the first authorâs previous result that the oscillatory parameter regime of the gene regulatory circuits can be rigorously explored by the local stability analysis of a unique equilibrium. The local stability analysis then leads to the first engineering principle that the circuit components, or genes, should be chosen so that the kinetic profiles of the circuit components are similar to each other. Using a homogeneous oscillator model, we further discuss how to reduce the cell-to-cell variability of the oscillators that is caused by intrinsic noise.  +
The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, computational protein design was used to create functional variants of qacR, a tetR family repressor, responsive to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. A computatio ally designed library was screened using an in vitro transcription-translation (TX-TL) system. Leads from the in vitro screen were characterized in vivo. Preliminary results demonstrate dose-dependent regulation of a downstream fluorescent reporter by vanillin. These repressor designs provide a starting point for the evolution of improved variants. We believe this process can serve as a framework for designing new sensors for other target compounds.  +
The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, variants of qacR, a tetR family repressor, were generated by computational protein design and screened in a cell-free transcription-translation (TX-TL) system for responsiveness to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. Promising candidates from the in vitro screen were further characterized in vitro and in vivo in a gene circuit. The screen yielded two qacR mutants that respond to vanillin both in vitro and in vivo. While the mutants exhibit some toxicity to cells, presumably due to off-target effects, they are prime starting points for directed evolution toward vanillin sensors with the specifications required for use in a dynamic control loop. We believe this process, a combination of the generation of variants coupled with in vitro screening, can serve as a framework for designing new sensors for other target compounds.  +
The pursuit of circuits and metabolic pathways of increasing complexity and robustness in synthetic biology will require engineering new regulatory tools. Feedback control based on relevant molecules, including toxic intermediates and environmental signals, would enable genetic circuits to react appropriately to changing conditions. In this work, variants of qacR, a tetR family repressor, were generated by compu- tational protein design and screened in a cell-free transcription-translation (TX-TL) system for responsiveness to a new targeted effector. The modified repressors target vanillin, a growth-inhibiting small molecule found in lignocellulosic hydrolysates and other industrial processes. Promising candidates from the in vitro screen were further characterized in vitro and in vivo in a gene circuit. The screen yielded two qacR mutants that respond to vanillin both in vitro and in vivo. We believe this process, a combination of the generation of variants coupled with in vitro screening, can serve as a framework for designing new sensors for other target compounds.  +
Lux-type quorum sensing systems enable communication in bacteria with only two protein components: a signal synthase and an inducible transcription activator. The simplicity of these systems makes them a popular choice for engineering collaborative behaviors in synthetic bacterial consortia, such as photographic edge detection and synchronized oscillation. To add to this body of work, we propose a pulsatile communication circuit that enables dynamic patterning and long-distance communication analogous to action potentials traveling through nerve tissue. We employed a model-driven design paradigm involving incremental characterization of in vivo design candidates with increasing circuit complexity. Beginning with a simple inducible reporter system, we screened a small number of circuits varying in their promoter and ribosomal binding site strengths. From this candidate pool, we selected a candidate to be the seed network for the subsequent round of more complex circuit variants, likewise variable in promoter and RBS strengths. The selection criteria at each level of complexity is tailored to optimize a different desirable performance characteristic. By this approach we individually optimized reporter signal-to-background ratio, pulsatile response to induction, and quiescent basal transcription, avoiding large library screens while ensuring robust performance of the composite circuit.  +
When used as part of a hybrid controller, finite-memory strategies synthesized from linear-time temporal logic (LTL) specifications rely on an accurate dynamics model in order to ensure correctness of trajectories. In the presence of uncertainty about the underlying model, there may exist unexpected trajectories that manifest as unexpected transitions under control of the strategy. While some disturbances can be captured by augment- ing the dynamics model, such approaches may be con- servative in that bisimulations may fail to exist for which strategies can be synthesized. In this paper, we consider games of the GR(1) fragment of LTL, and we character- ize the tolerance of hybrid controllers to perturbations that appear as unexpected jumps (transitions) to states in the discrete strategy part of the controller. As a first step, we show robustness to certain unexpected transi- tions that occur in a finite manner, i.e., despite a certain number of unexpected jumps, the sequence of states ob- tained will still meet a stricter specification and hence the original specification. Additionally, we propose al- gorithms to improve robustness by increasing tolerance to additional disturbances. A robot gridworld example is presented to demonstrate the application of the de- veloped ideas and also to perform empirical analysis.  +
We define a notion of controllability for mechanical systems which determines the configurations which are accessible from a given configuration. We derive sufficient conditions for this notion of controllability in terms of the given inputs, their Lie brackets, and their covariant derivatives.  +
In this paper we consider a state estimation problem over a wireless sensor network. A fusion center dynamically forms a local multi-hop tree of sensors and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. Using estimation quality as a metric, two communication schemes are studied and compared. In scheme one, sensor nodes communicate measurement data to their parent nodes, while in scheme two, sensor nodes communicate their local state estimates to their parent nodes. We show that under perfect communication links, the two schemes produce the same estimate at the fusion center with unlimited computation at each sensor node; scheme one is always better than scheme two with limited computation. When data packet drops occur on the communication links, we show that scheme two always outperforms scheme one with unlimited computation; with limited computation, we show that there exists a critical packet arrival rate, above which, scheme one outperforms scheme two. Simulations are provided to demonstrate the two schemes under various circumstances.  +
This paper considers the problem of estimation over communication networks. Suppose a sensor is taking measurements of a dynamic process. However the process needs to be estimated at a remote location connected to the sensor through a network of communication links that drop packets stochastically. We provide a framework for computing the optimal performance in the sense of expected error covariance. Using this framework we characterize the dependency of the performance on the topology of the network and the packet dropping process. For independent and memoryless packet dropping processes we find the steady-state error for some classes of networks and obtain lower and upper bounds for the performance of a general network. We also illustrate how this framework can be used in the synthesis of networks for the purpose of estimation. Finally we find a necessary and sufficient condition for the stability of the estimate error covariance for general networks with spatially correlated and Markov type dropping process. This interesting condition has a max-cut interpretation.  +
In this work we consider a class of networked control systems (NCS) when the control signal is sent to the plant via a UDP-like communication protocol, the controller sends a communication packet to the plant across a lossy network but the controller.....  +
In this paper, we consider a discrete time state estimation problem over a packet-based network. In each discrete time step, the measurement is sent to a Kalman filter with some probability that it is received or dropped. Previous pioneering work on Kalman filtering with intermittent observation losses shows that there exists a certain threshold of the packet dropping rate below which the estimator is stable in the expected sense. In their analysis, they assume that packets are dropped independently between all time steps. However we give a completely different point of view. On the one hand, it is not required that the packets are dropped independently but just that the information gain pi_g, defined to be the limit of the ratio of the number of received packets n during N time steps as N goes to infinity, exists. On the other hand, we show that for any given pi_g, as long as pi_g > 0, the estimator is stable almost surely, i.e. for any given epsilon > 0 the error covariance matrix P{k is bounded by a finite matrix M, with probability 1 â epsilon. Given an error tolerance M, pi_g can in turn be found. We also give explicit formula for the relationship between M and epsilon.  +
In this paper we evaluate the actuator rate requirements for control of rotating stall using a bleed valve and provide tools for predicting these requirements. Modification of both the stable and unstable parts of the compressor characteristic via addition of continuous air injection serves to reduce the requirement of a bleed valve used for the purpose of rotating stall stabilization. Analytical tools based on low order models (2-3 states) and simulation tools based on a reduced order model (37 states) are described. A bleed actuator rate limit study is presented to compare the actuator requirements predicted by theory, simulation, and experiment. The comparisons show that the predictions obtained from theory and simulations share the same trend as the experiments, with increasing accuracy as the complexity of the underlying model increases. Some insights on the design of a bleed-compressor pair are given.  +
This paper provides analytical results regarding the stability of linear discrete-time systems with stochastic delays. Necessary and sufficient stability conditions are derived by using the second moment dynamics which can be used to draw stability charts. The results are applied to a simple connected vehicle system where the stability regions are com- pared to those given by the mean dynamics. Our results reveal some fundamental limitations of connected cruise control which becomes more significant as the packet drop ratio increases.  +
In this paper, a cascade discrete-continuous state estimator on a partial order is proposed and its existence investigated. The continuous state estimation error is bounded by a monotonically nonincreasing function of the discrete state estimation error, with both the estimation errors converging to zero. This work shows that the lattice approach to estimation is general as the proposed estimator can be constructed for any observable and discrete state observable system. The main advantage of using the lattice approach for estimation becomes clear when the system has monotone properties that can be exploited in the estimator design. In such a case, the computational complexity of the estimator can be drastically reduced and tractability can be achieved. Some examples are proposed to illustrate these ideas.  +
In this paper various design techniques are applied to the trajectory tracking problem for a mobile robot with trailers. Using simulations and experiments, we evaluate linear and nonlinear designs on the basis of implementation issues, stability and performance. After a careful design of their gains, the various feedback controllers have very close performance measures. In both the simulations and the experiments, all the controllers show a strong dependence on the knowledge of the reference trajectory. The flatness of the system is exploited in precomputing this quantity.  +
The motion of microorganisms as well as of tiny robotic swimmers for biomedical applications is governed by low Reynolds number (Re) hydrodynamics, where viscous effects dominate and inertial effects are negligible. This paper presents experimental results that verify theoretical predictions of our recent work which analyzed the dynamics and stability of a low-Re swimmer near a plane wall. The experimental setup uses macro-scale swimmer prototypes which are propelled by rotating cylinders in highly viscous silicone oil. The motion was recorded by a video camera and position measurements were taken by an optical tracking system. The results show good qualitative agreement with our recent theoretical predictions.  +
This paper presents an experimental investigation of the effects of air injection on the rotating stall instability in a low speed axial compressor. Two experiments concerning air injection were tried. The first experiment used a continuous forcing perpendicular to the flow in the same or opposite direction of the tip velocity. The results show a dramatic difference between the two directions, with opposite direction forcing causing a significant increase in performance, and same direction forcing causing a significant decrease in performance. This result contradicts the Emmons stall propagation model. The second experiment investigated the differences with respect to different frequencies of air injection, with the injector pointed at the fan, parallel to the flow. We found that the change in the compressor characteristic in the unstalled region was highly dependent upon the forcing frequency with the maximum change occurring near the frequency of stall.  +
In this paper we apply some recently developed control laws for stabilization of mechanical systems with nonholonomic constraints to an experimental system consisting of a mobile robot towing a trailer. We verify the applicability of various control laws which have appeared in the recent literature, and compare the performance of these controllers in an experimental setting. In particular, we show that time-periodic, non-smooth controllers can be used to achieve exponential stability of a desired equilibrium configuration, and that these controllers outperform smooth, time-varying control laws. We also point out several practical considerations which must be taken into account when implementing these controllers.  +
Many algorithms have been proposed in the literature for control of multi-fingered robot hands. This paper compares the performance of several of these algorithms, as well as some extensions of more conventional manipulator control laws, in the case of planar grasping. A brief introduction to the subject of robot hands and the notation used in this paper is included.  +
This dissertation lays the foundation for practical exponential stabilization of driftless control systems. Driftless systems have the form '"`UNIQ-MathJax562-QINU`"'. Such systems arise when modeling mechanical systems with nonholonomic constraints. In engineering applications it is often required to maintain the mechanical system around a desired configuration. This task is treated as a stabilization problem where the desired configuration is made an asymptotically stable equilibrium point. The control design is carried out on an approximate system. The approximation process yields a nilpotent set of input vector fields which, in a special coordinate system, are homogeneous with respect to a non-standard dilation. Even though the approximation can be given a coordinate-free interpretation, the homogeneous structure is useful to exploit: the feedbacks are required to be homogeneous functions and thus preserve the homogeneous structure in the closed-loop system. The stability achieved is called {\em $\rho$-exponential stability}. The closed-loop system is stable and the equilibrium point is exponentially attractive. This extended notion of exponential stability is required since the feedback, and hence the closed-loop system, is not Lipschitz. However, it is shown that the convergence rate of a Lipschitz closed-loop driftless system cannot be bounded by an exponential envelope. <p> The synthesis methods generate feedbacks which are smooth on \rminus. The solutions of the closed-loop system are proven to be unique in this case. In addition, the control inputs for many driftless systems are velocities. For this class of systems it is more appropriate for the control law to specify actuator forces instead of velocities. We have extended the kinematic velocity controllers to controllers which command forces and still $\rho$-exponentially stabilize the system. <p> Perhaps the ultimate justification of the methods proposed in this thesis are the experimental results. The experiments demonstrate the superior convergence performance of the $\rho$-exponential stabilizers versus traditional smooth feedbacks. The experiments also highlight the importance of transformation conditioning in the feedbacks. Other design issues, such as scaling the measured states to eliminate hunting, are discussed. The methods in this thesis bring the practical control of strongly nonlinear systems one step closer. <p>  
This paper brings together results from a number of different areas in control theory to provide an algorithm for the synthesis of locally exponentially stabilizing control laws for a large class of driftless nonlinear control systems. The exponential stabilization relies on the use of feedbacks which render the closed loop vector field homogeneous with respect to a dilation. These feedbacks are generated from a modification of Pomet's algorithm for smooth feedbacks. Converse Liapunov theorems for time-periodic homogeneous vector fields guarantee that local exponential stability is maintained in the presence of higher order (with respect to the dilation) perturbing terms. <p>  +
This paper describes an approach for extending (time-varying) exponential stabilizers for nonholonomic systems from controllers which command input velocity to controllers which command input torques. Due to the nondifferentiable nature of exponential stablizers, additional structure is required in order to ensure that the extended controllers generate continuous control actions. In this paper we show how to extend homogeneous controllers which use a nonstandard dilation adapted to the problem.  +
We describe the structure of connected graphs with the minimum and maximum average distance, radius, diameter, betweenness centrality, efficiency and resistance distance, given their order and size. We find tight bounds on these graph qualities for any arbitrary number of nodes and edges and analytically derive the form and properties of such networks.  +
F
Fault tolerance and safety verification of control systems that have state estimation uncertainty are essential for the success of autonomous robotic systems. A software control architecture called Mission Data System, developed at the Jet Propulsion Laboratory, uses goal networks as the control program for autonomous systems. Certain types of goal networks can be converted into linear hybrid systems and verified for safety using existing symbolic model checking software. A process for calculating the probability of failure of some verifiable goal networks due to state estimation uncertainty is presented. Extensions of this procedure to include other types of uncertainties are discussed, and example problems are presented to illustrate these procedures.  +
Increased complexity in cyber-physical systems calls for modular system design methodologies that guarantee correct and reliable behavior, both in normal operations and in the presence of failures. This paper aims to extend the contract-based design approach using a directive-response architecture to enable reactivity to failure scenarios. The architecture is demonstrated on a modular automated valet parking (AVP) system. The contracts for the different components in the AVP system are explicitly defined, implemented, and validated against a Python implementation.  +
Modern safety-critical systems are difficult to formally verify, largely due to their large scale. In particular, the widespread use of lookup tables in embedded systems across diverse industries, such as aeronautics and automotive systems, create a critical obstacle to the scala- bility of formal verification. This paper presents a novel approach for the formal verification of large-scale systems with lookup tables. We use a learning-based technique to automatically learn abstractions of the lookup tables and use the abstractions to then prove the desired property. If the verification fails, we propose a falsification heuristic to search for a violation of the specification. In contrast with previous work on lookup table verification, our technique is completely automatic, making it ideal for deployment in a production environment. To our knowledge, our approach is the only technique that can automatically verify large-scale systems lookup with tables. We illustrate the effectiveness of our technique on a benchmark which cannot be handled by the commer- cial tool SLDV, and we demonstrate the performance improvement provided by our technique.  +
Aircraft operate in different modes during flight, corresponding to different flight conditions and control schemes. We use differential flatness of an approximate model of the pitch dynamics of a thrust vectored aircraft to achieve fast switching between those modes. We investigate some methods to compensate for the perturbations to flatness. Simulations and experimental data are provided to validate the approach.  +
In systems and synthetic biology, it is common to build chemical reaction network (CRN) models of biochemical circuits and networks. Although automation and other high-throughput techniques have led to an abundance of data enabling data-driven quantitative modeling and parameter estimation, the intense amount of simulation needed for these methods still frequently results in a computational bottleneck. Here we present bioscrape (Bio-circuit Stochastic Single-cell Reaction Analysis and Parameter Estimation) - a Python package for fast and flexible modeling and simulation of highly customizable chemical reaction networks. Specifically, bioscrape supports deterministic and stochastic simulations, which can incorporate delay, cell growth, and cell division. All functionalities - reaction models, simulation algorithms, cell growth models, and partioning models - are implemented as interfaces in an easily extensible and modular object-oriented framework. Models can be constructed via Systems Biology Markup Language (SBML), a simple internal XML language, or specified programmatically via a Python API. Simulation run times obtained with the package are comparable to those obtained using C code - this is particularly advantageous for computationally expensive applications such as Bayesian inference or simulation of cell lineages. We first show the package’s simulation capabilities on a variety of example simulations of stochastic gene expression. We then further demonstrate the package by using it to do parameter inference on a model of integrase enzyme-mediated DNA recombination dynamics with experimental data. The bioscrape package is publicly available online (https://github.com/ananswam/bioscrape) along with more detailed documentation and examples.  +
One of the challenges in designing the next genera- tion of robots operating in non-engineered environments is that there seems to be an infinite amount of causes that make the sensor data unreliable or actuators ineffective. In this paper, we discuss what faults are possible to detect using zero modeling effort: we start from uninterpreted streams of observations and commands, and without a prior knowledge of a model of the world. We show that in sensorimotor cascades it is possible to define static faults independently of a nominal model. We define an information-theoretic usefulness of a sensor reading and we show that it captures several kind of sensorimotor faults frequently encountered in practice. We particularize these ideas to the case of BDS/BGDS models, proposed in previous work as suitable candidates for describing generic sensorimotor cascades. We show several examples with camera and range-finder data, and we discuss a possible way to integrate these techniques in an existing robot software architecture.  +
This paper deals with fault-tolerant controller design for linear time-invariant (LTI) systems with multiple actuators. Given some critical subsets of the actuators, it is assumed that every combination of actuators can fail as long as the set of the remaining actuators includes one of these subsets. Motivated by electric power systems and biological systems, the goal is to design a controller so that the closed-loop system satisfies two properties: (i) stability under all permissible sets of faults and (ii) better performance after clearing every subset of the existing faults in the system. It is shown that a state-feedback controller satisfying these properties exists if and only if a linear matrix inequality (LMI) problem is feasible. This LMI condition is then transformed into an optimal-control condition, which has a useful interpretation. The results are also generalized to output-feedback and decentralized control cases. The efficacy of this work is demonstrated by designing fault-tolerant speed governors for a power system. The results developed here can be extended to more general types of faults, where each fault can possibly affect all state-space matrices of the system.  +
This paper proposes a method to determine trajectories of dynamic systems that steer between two end points while satisfying linear inequality constraints arising from limits on states and inputs. The method exploits the structure of the dynamic system written in a higher-order form to explicitly eliminate the state equations. The feasible trajectories of the dynamic system are sought within a characterization with a finite sum of mode functions. In this paper, the linear inequalities on inputs and states are replaced by a finite set of linear inequalities on the mode coefficients. This step changes the problem of trajectory generation into finding a convex polytope enclosed by the linear inequalities on the mode coefficients. A procedure is then developed to efficiently find the vertices of this bounding polytope. It is demonstrated in this paper that this method can generate feasible trajectories of the system in real-time and can quickly update the trajectories as the terminal conditions are changed. The procedure is demonstrated numerically by two examples. The results of one of the examples is implemented in hardware to explore the issues of real-time planning and control.  +
In this paper we consider nonlinear systems with steady-state or Hopf bifurcations for which the bifurcated modes are linearly uncontrollable. The goal is to find state feedbacks such that the bifurcation for the closed loop system is supercritical, and at the same time, the linearly controllable subsystem is asymptotically stable. Necessary and sufficient conditions for the non-existence of sufficiently smooth state feedbacks have been obtained under certain nondegeneracy conditions. For the cases when those conditions are not satisfied, we give explicit constructions of the feedbacks. The construction has the following separation property: for any linear state feedback such that the controllable subsystem is asymptotically stable, we could construct gains in the nonlinear state feedbacks such that the closed loop system is asymptotically stable at the bifurcation point.  +
Classification of stabilizability is obtained for multi-input nonlinear systems possessing a simple steady-state or Hopf bifurcation with the critical mode being linearly uncontrollable. Stabilizability is defined as the existence of a sufficiently smooth state feedback such that the bifurcation for the closed loop system is supercritical, and in the meantime, the linearly controllable modes are locally asymptotically stable. Necessary and sufficient conditions of stabilizability are derived under certain nondegeneracy conditions. Explicit construction of stabilizing feedbacks is obtained for the cases when the system is stabilizable.  +
This paper focuses on RNA flux regulation for in vitro synthetic gene networks and considers architectures that can be scaled to an arbitrary number of species. Feedback loops are designed based on negative autoâregulation (which can minimize the potentially harmful amount of molecules not used to form useful products) and crossâactivation (which can maximize the overall output flux): transcription rate matching can be achieved through proper feedback constants; negative feedback is faster and maintains stability. A possible experimen- tal implementation of a three and four genes negative feedback architecture is also numerically studied.  +
Noise is indispensible to key cellular activities, including gene expression coordination and probabilistic differentiation. Stochastic models, such as the chemical master equation (CME), are essential to model noise in the levels of cellular components. In the CME framework, each state is associated with the molecular counts of all component species, and specifies the probability for the system to have that set of molecular counts. Analytic solutions to the CME are rarely known but can bring exciting benefits. For instance, simulations of biochemical reaction networks that are multiscale in time can be sped up tremendously by incorporating analytic solutions of the slow time-scale dynamics. Ana- lytic solutions also enable the design of stationary distributions with properties such as the modality of the distribution, the mean expression level, and the level of noise. One way to derive the analytic steady state response of a biochemical reaction network was re- cently proposed by (Mélykúti et al. 2014). The paper recursively glues simple state spaces together, for which we have analytic solutions, at one or two states. <p> In this work, we explore the benefits and limitations of the gluing technique proposed by Mélykúti et al., and introduce recursive algorithms that use the technique to solve for the analytic steady state response of stochastic biochemical reaction networks. We give formal characterizations of the set of reaction networks whose state spaces can be obtained by carrying out single-point gluing of paths, cycles or both sequentially. We find that the dimension of the state space of a reaction network equals the maximum number of linearly independent reactions in the system. We then characterize the complete set of stochastic biochemical reaction networks that have elementary reactions and two-dimensional state spaces. As an example, we propose a recursive algorithm that uses the gluing technique to solve for the steady state response of a mass-conserving system with two connected monomolecular reversible reactions. Even though the gluing technique can only construct finite state spaces, we find that, by taking the size of a finite state space to infinity, the steady state response can converge to the analytic solution on the resulting infinite state space. Finally, we illustrate the aforementioned ideas with the example of two interconnected transcriptional components, which was first studied by (Ghaemi and Del Vecchio 2012).  
In this paper, we consider the optimal control of time-scalable systems. The time-scaling property is shown to convert the PDE associated with the Hamilton-Jacobi-Bellman (HJB) equation to a purely spatial PDE. Solution of this PDE yields the value function at a fixed time, and that solutio n can be scaled to find the value function at any point in time. Furthermore, in certain cases the unscaled control law stabilizes the system, and the unscaled value function acts as a Lyapunov function for that system. For the example of the nonholonomic integrator, this PDE is solved, and the resulting optimal trajectories coincide with the known solution to that problem.  +
Flat systems, an important subclass of nonlinear control systems introduced via differential-algebraic methods, are defined in a differential geometric framework. We utilize the infinite dimensional geometry developed by Vinogradov and coworkers: a control system is a diffiety, or more precisely, an ordinary diffiety, i.e. a smooth infinite-dimensional manifold equipped with a privileged vector field. After recalling the definition of a Lie-Backlund mapping, we say that two systems are equivalent if they are related by a Lie-Backlund isomorphism. Flat systems are those systems which are equivalent to a controllable linear one. The interest of such an abstract setting relies mainly on the fact that the above system equivalence is interpreted in terms of endogenous dynamic feedback. The presentation is as elementary as possible and illustrated by the VTOL aircraft.  +
A feedback controller closes the loop from vision to wing motion to stabilize forward flight in a simulation of Drosophila Melanogaster.  +
We have approached the problem of reverse engineering the flight control mechanism of the fruit fly by studying the dynamics of the responses to a visual stimulus during takeoff. Building upon a prior framework we seek to understand the strategies employed by the animal to stabilize attitude and orientation during these evasive, highly dynamical maneuvers. As a first step, we consider the dynamics from a gray-box perspective: examining lumped forces produced by the insect's legs and wings. The reconstruction of the flight initiation dynamics, based on the unconstrained motion formulation for a rigid body, allows us to assess the fly's responses to a variety of initial conditions induced by its jump. Such assessment permits refinement by using a visual tracking algorithm to extract the kinematic envelope of the wings in order to estimate lift and drag forces, and recording actual leg-joint kinematics and using them to estimate jump forces. In this paper we present the details of our approach in a comprehensive manner including the salient results.  +
The prolific rise in autonomous systems has led to questions regarding their safe instantiation in real-world scenarios. Failures in safety-critical contexts such as human-robot interactions or even autonomous driving can ultimately lead to loss of life. In this context, this paper aims to provide a method by which one can algorithmically test and evaluate an autonomous system. Given a black-box autonomous system with some operational specifications, we construct a minimax problem based on control barrier functions to generate a family of test parameters designed to optimally evaluate whether the system can satisfy the specifications. To illustrate our results, we utilize the Robotarium as a case study for an autonomous system that claims to satisfy waypoint navigation and obstacle avoidance simultaneously. We demonstrate that the proposed test synthesis framework systematically finds those sequences of events (tests) that identify points of system failure.  +
Model checking is a widely used technique for formal verification of distributed systems. It works by effectively examining the complete reachable state space of a model in order to determine whether the system satisfies its requirements or desired properties. The complexity of an autonomous vehicle system, however, renders model checking of the entire system infeasible due to the state explosion problem. In this paper, we illustrate how to exploit the structure of the system to systematically decompose the overall system-level requirements into a set of component-level requirements. Each of the components can then be model checked separately. A case study is presented where we formally verify the state consistency between different software modules of Alice, an autonomous vehicle developed by the California Institute of Technology for the 2007 DARPA Urban Challenge.  +
In this paper, we generalize a recently proposed method for model reduction of linear systems to the frequencyweighted case. The method uses convex optimization and can be used both with sample data and exact models. We also derive simple a priori bounds on the frequency-weighted error. We combine the method with a rank-minimization heuristic, to approximate multi-inputÂmulti-output systems. We also present two applications  environment compensation and simpli�cation of interconnected models  where we argue the proposed methods are useful.  +
The field of control provides the principles and methods used to design physical and information systems that maintain desirable performance by sensing and automatically adapting to changes in the environment. As we begin the 21st Century, the opportunities to apply control principles and methods are exploding. New developments in this increasingly information rich world will require a significant expansion of the basic tool sets of control. This article summarizes the main findings and recommendations of the Panel on Future Directions in Control, Dynamics, and Systems, which has recently released its report. The report spells out some of the prospects for control in the current and future technological environment, describes the role the field will play in military, commercial, and scientific applications over the next decade, and recommends actions required to enable new breakthroughs in engineering and technology through application of control research.  +
This paper summarizes the findings and recommendations of a recent panel on Future Directions in Control, Dynamics, and Systems, sponsored by the US Air Force Office of Scientific Research. A set of grand challenges that illustrate some of the recommendations and opportunities are provided. Finally, the paper describes two new courses being developed at Caltech that are aligned with the recommendations of the report.  +
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This paper gives a survey of some recent results on control of systems with magnitude and rate limits, motivated by problems in real-time trajectory generation and tracking for unmanned aerial vehicles. Two problems are considered: stabilization using ``nonlinear wrappers'' to rescale a given control law and real-time trajectory generation using differential flatness. For both problems, simplified versions of the general problem are studied using tools from differential geometry and nonlinear control to give insights into the limitations imposed by magnitude and rate limits and provide insights into constructive solutions to the trajectory generation and tracking problems.  +
Manipulation of particles suspended in fluids is crucial for many applications, such as precision machining, chemical processes, bio-engineering, and self-feeding of microorganisms. In this paper, we study the problem of particle manipulation by cyclic fluid boundary excitations from a geometric-control viewpoint. We focus on the simplified problem of manipulating a single particle by generating controlled cyclic motion of a circular rigid body in a two-dimensional perfect fluid. We show that the drift in the particle location after one cyclic motion of the body can be interpreted as the geometric phase of a connection induced by the system's hydrodynamics. We then formulate the problem as a control system, and derive a geometric criterion for its nonlinear controllability. Moreover, by exploiting the geometric structure of the system, we explicitly construct a feedback-based gait that results in attraction of the particle towards the rigid body. We argue that our gait is robust and model-independent, and demonstrate it in both perfect fluid and Stokes fluid.  +
Robotic locomotion is based in a variety of instances upon cyclic changes in the shape of a robot mechanism. Certain variations in shape exploit the constrained nature of a robot's interaction with its environment to generate net motion. This is true for legged robots, snakelike robots, and wheeled mobile robots undertaking maneuvers such as parallel parking. In this paper we explore the use of tools from differential geometry to model and analyze this class of locomotion mechanisms in a unified way. In particular, we describe locomotion in terms of the geometric phase associated with a connection on a principal bundle, and address issues such as controllability and choice of gait. We also provide an introduction to the basic mathematical concepts which we require and apply the theory to numerous example systems.  +
Differential geometry and nonlinear control theory provide essential tools for studying motion generation in robot systems. Two areas where progress is being made are motion planning for mobile robots on the factory floor (or on the surface of Mars), and control of highly articulated robots---such as multifingered robot hands and robot ``snakes''---for medical inspection and manipulation inside the gastrointestinal tract. A common feature of these systems is the role of constraints on the behavior of the system. Typically, these constraints force the instantaneous velocities of the system to lie in a restricted set of directions, but do not actually restrict the reachable configurations of the system. A familiar example in which this geometric structure can be exploited is parallel parking of an automobile, where periodic motion in the driving speed and steering angle can be used to achieve a net sideways motion. By studying the geometric nature of velocity constraints in a more general setting, it is possible to synthesize gaits for snake-like robots, generate parking and docking maneuvers for automated vehicles, and study the effects of rolling contacts on multifingered robot hands. As in parallel parking, rectification of periodic motions in the control variables plays a central role in the techniques which are used to generation motion in this broad class of robot systems.  +
The paper studies the problem which we refer to as geometric trajectory filtering, where only trajectories that satisfy the local safety constraints are selected from a library of trajectories. The goal is to speed up primitive-based motion planning while still maintaining a relatively a large collection of motion primitives. One way to solve this problem is to obtain a proper (preferably smooth) function, referred to as the containment indicator function, that describes the shape of the free space. To construct the containment indicator function for an arbitrary shape, the paper uses conformal mapping to transform the original shape of interest to a simpler target shape (e.g. disk, rectangle), which can then be characterized by elementary functions. Computational methods for finding the desired conformal maps are studied. It is shown that they can be formulated as convex optimization problems, whose solution can be obtained efficiently.  +
In this paper we consider the problem of network reconstruction, with applications to biochemical reaction networks. In particular, we consider the problem of global network reconstruction when there are a limited number of sensors that can be used to simultaneously measure state information. We introduce dynamical structure functions as a way to formulate the network reconstruction problem and motivate their usage with an example physical system from synthetic biology. In particular, we argue that in synthetic biology research, network verification is paramount to robust circuit operation and thus, network reconstruction is an invaluable tool. Nonetheless, we argue that existing approaches for reconstruction are hampered by limited numbers of biological sensors with high temporal resolution. In this way, we motivate the global network reconstruction problem using partial network information and prove that by performing a series of reconstruction experiments, where each experiment reconstructs a subnetwork dynamical structure function, the global dynamical structure function can be recovered in most cases. We illustrate these reconstruction techniques on a recently developed four gene biocircuit, an event detector, and show that it is capable of differentiating the temporal order of input events.  +
Control of vehicle formations has emerged as a topic of significant interest to the controls community. In this paper, we merge tools from graph theory and control theory to derive stability criteria for formation stabilization. The interconnection between vehicles (i.e., which vehicles are sensed by other vehicles) is modeled as a graph, and the eigenvalues of the Laplacian matrix of the graph are used in stating a Nyquist-like stability criterion for vehicle formations. The location of the Laplacian eigenvalues can be correlated to the graph structure, and therefore used to identify desirable and undesirable formation interconnection topologies.  +
Grasping with flexible fingers presents an attractive approach for certain robotic tasks. Its implementation requires simultaneous position and force control of flexible manipulators, an area about which there is little information in the literature. This paper presents an initial effort at designing controllers for flexible link robots to control both position and force. The analysis is done on a two degree-of-freedom two-link manipulator with the last link flexible. A control strategy is proposed and asymptotic stability is proved. Results from using this control law in simulations and on an experimental setup are presented.  +
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Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems.  +
We propose a method for eliminating variables from component specifications during the decomposition of GR(1) properties into contracts. The variables that can be eliminated are identified by parameterizing the communication architecture to investigate the dependence of realizability on the availability of information. We prove that the selected variables can be hidden from other components, while still expressing the resulting specification as a game with full information with respect to the remaining variables. The values of other variables need not be known all the time, so we hide them for part of the time, thus reducing the amount of information that needs to be communicated between components. We improve on our previous results on algorithmic decomposition of GR(1) properties, and prove existence of decompositions in the full information case. We use semantic methods of computation based on binary decision diagrams. To recover the constructed specifications so that humans can read them, we implement exact symbolic minimal covering over the lattice of integer orthotopes, thus deriving minimal formulae in disjunctive normal form over integer variable intervals.  +
We consider the problem of synthesizing robot controllers to realize a task that unpredictably changes with time. Tasks are formally expressed in the GR(1) fragment of temporal logic, in which some of the variables are set by an adversary. The task changes by the addition or removal of goals, which occurs online (i.e., at run-time). We present an algorithm for mending control strategies to realize tasks after the addition of goals, while avoiding global re-synthesis of the strategy. Experiments are presented for a planar surveillance task in which new regions of interest are incrementally added. Run-times are empirically shown to be extremely favorable compared to re-synthesizing from scratch. We also present an algorithm for mending control strategies for the removal of goals. While in this setting the original strategy is still feasible (as we prove), our algorithm provides a more satisfying solution by âtightening loose ends.â Both algorithms are shown to yield so-called reach annotations, and thus the control strategies are easily amenable to other algorithms concerning incremental synthesis, e.g., as in previous work by the authors for robot navigation in uncertain environments.  +
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The rules that govern decision making in systems controlled by humans are often simple to describe. However, deriving these rules from the actions of a group can be very difficult, making human behavior hard to predict. We develop an algorithm to determine the rules implemented by drivers at a traffic intersection by observing the trajectories of their cars. We applied such algorithm to a traffic intersection scenario reproduced in the Caltech multi-vehicle lab, with human subjects remotely driving kinematic robots. The results obtained on these data suggest that this kind of human behavior is to some extent predictable on our data set, and different subjects implement similar rules.  +
When used as part of a hybrid controller, finite- memory strategies synthesized from LTL specifications rely on an accurate dynamics model in order to ensure correctness of trajectories. In the presence of uncertainty about this underlying model, there may exist unexpected trajectories that manifest as unexpected transitions under control of the strategy. While some disturbances can be captured by augmenting the dynamics model, such approaches may be conservative in that bisimulations may fail to exist for which strategies can be synthesized. In this paper, we characterize the tolerance of such hybrid controllers - synthesized for generalized reactivity(1) specifications- to disturbances that appear as unexpected jumps (transitions) to states in the discrete strategy part of the con- troller. As a first step, we show robustness to certain unexpected transitions that occur in a finite-manner, i.e., despite a certain number of unexpected jumps, the sequence of states obtained will still meet a stricter specification and hence the original specification. Additionally, we propose algorithms to improve robustness by increasing tolerance to additional disturbances. A robot gridworld example is presented to demonstrate the application of the developed ideas and also to obtain empirical computational and memory cost estimates.  +
The operational amplifier (OPAMP) is a very useful insulation module in electric circuits to avoid loading effect (retroactivity). In synthetic biological circuits, we also have the same retroactivity problem, in which the biomolecular systems are not always modular due to downstream components. The output of the upstream component will be affected as the downstream component sequesters that output, which in turn impedes the process of constructing more complex biocircuits. To address this obstacle, the retroactivity needs to be attenuated by implementing a similar OPAMP device using biocircuits. Previous theoretical papers suggested a potential function of a phosphorylation based circuit in providing the feature of atten- uating retroactivity. Here we presented a successful prototyping and implementation of such a phosphorylation-based insulator (PBI) in an in vitro cell-free transcription-translation system (TX- TL). We demonstrated that retroactivity also exists in TX-TL system, if not stronger, by testing a simple negative regulation circuit. Besides we showed that the TX-TL system contains all the protein, DNA components and other resources required for the PBI circuit to work properly. We then demonstrated that the PBI circuit helps minimizing the loading effect to less than 10% compared to control circuit. With this preliminary PBI circuit design, attenuation of retroactivity while connecting two modules in vitro becomes possible. In concert with another paper from our group (E. Yeung, S. Guo, R. Murray QBIO2014) which used system identification to estimate all three essential parameters in a simplified PBI model, we showed that the simulations based on these parameters match the experimental data very well and provide an interesting insight into future designs.  +
Vehicles in formation often lack global information regarding the state of all the vehicles, a deficiency which can lead to instability and poor performance. In this paper, we demonstrate how exchange of minimal amounts of information between vehicles can be designed to realize a dynamical system which supplies each vehicle with a shared reference trajectory. When the information flow law is placed in the control loop, a separation principle is proven which guarantees stability of the formation and convergence of the information flow law regardless of the information flow topology.  +
This paper describes the implementation of an in- terface connecting the two tools : the JPL SCA (Statechart Autocoder) and TuLiP (Temporal Logic Planning Toolbox) to enable the automatic synthesis of low level implementation code directly from formal specifications. With system dynamics, bounds on uncertainty and formal specifications as inputs, TuLiP synthesizes Mealy machines that are correct-by-construction. An interface is built that automatically translates these Mealy machines into UML statecharts. The SCA accepts the UML statecharts (as XML files) to synthesize flight-certified2 implementation code. The functionality of the interface is demonstrated through three example systems of varying com- plexity a) a simple thermostat b) a simple speed controller for an autonomous vehicle and c) a more complex speed controller for an autonomous vehicle with a map-element. In the thermostat controller, there is a specification regarding the desired temperature range that has to be met despite disturbance from the environment. Similarly, in the speed-controllers there are specifications about safe driving speeds depending on sensor health (sensors fail unpredictably) and the map-location. The significance of these demonstrations is the potential circumventing of some of the manual design of statecharts for flight software/controllers. As a result, we expect that less testing and validation will be necessary. In applications where the products of synthesis are used alongside manually designed components, extensive testing or new certificates of correctness of the composition may still be required.  +
Motivated by exploration of communication- constrained underground environments using robot teams, we study the problem of planning for intermittent connectivity in multi-agent systems. We propose a novel concept of information-consistency to handle situations where the plan is not initially known by all agents, and suggest an integer linear program for synthesizing information-consistent plans that also achieve auxiliary goals. Furthermore, inspired by network flow problems we propose a novel way to pose connectivity constraints that scales much better than previous methods. In the second part of the paper we apply these results in an exploration setting, and propose a clustering method that separates a large exploration problem into smaller problems that can be solved independently. We demonstrate how the resulting exploration algorithm is able to coordinate a team of ten agents to explore a large environment.  +
Ensuring safety through set invariance has proven a useful method in a variety of applications in robotics and control. However, finding analytical expressions for maximal invariant sets, so as to maximize the operational freedom of the system without compromising safety, is notoriously difficult for high-dimensional systems with input constraints. Here we present a generic method for characterizing invariant sets of nth-order integrator systems, based on analyzing roots of univariate polynomials. Additionally, we obtain analytical expressions for the orders n <= 4. Using differential flatness we subsequently leverage the results for the n = 4 case to the problem of obstacle avoidance for quadrotor UAVs. The resulting controller has a light computational footprint that showcases the power of finding analytical expressions for control-invariant sets.  +
Neural networks in real-world applications have to satisfy critical properties such as safety and reliability. The analysis of such properties typically involves extracting informa- tion through computing pre-images of neural networks, but it is well-known that explicit computation of pre-images is intractable. We introduce new methods for computing compact symbolic abstractions of pre-images. Our approach relies on computing approximations that provably overapproximate and underapproximate the pre-images at all layers. The abstraction of pre-images enables formal analysis and knowl- edge extraction without modifying standard learning algo- rithms. We show how to use inverse abstractions to automatically extract simple control laws and compact representations for pre-images corresponding to unsafe outputs. We illustrate that the extracted abstractions are often interpretable and can be used for analyzing complex properties.  +
A computationally efficient technique for the numerical solution of optimal control problems is discussed. This method utilizes tools from nonlinear control theory to transform the optimal control problem to a new, lower dimensional set of coordinates. It is hypothesized that maximizing the relative degree is directly related to minimizing the computation time. Firm evidence of this hypothesis is given. Results are presented using the Nonlinear Trajectory Generation (NTG) software package.  +
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We study the dynamics of the relative motion of satellites in the gravitational field of the Earth, including the effects of the bulge of the Earth (the $J_2$ effect). Using Routh reduction and dynamical systems ideas, a method is found that locates orbits such that the cluster of satellites remains close with very little dispersing, even with no controls. The use of controls in the context of this natural dynamics is studied to maintain and achieve precision formations.  +
The cost of the great expressivity of motion planning subject to temporal logic formulae is intractability. Recent advances in sampling-based methods seem to be only applicable to âlow-levelâ control. The problem of realizing âhigh-levelâ controllers that satisfy a temporal logic specification does not readily admit approximations, unless the notion of correctness is relaxed as might be achieved with probabilistic variants of temporal logics. In this paper, we argue that not all possible environment (uncontrolled) behaviors need to be explicitly planned for, but rather short-time strategies can be generated online while maintaining global correctness. We achieve this by separating feasibility from controller synthesis, using a metric from the underlying continuous state space to ensure short-time strategies chained together provide globally correct behavior.  +
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In this paper, we consider Kalman filtering over a packet-delaying network. Given the probability distribution of the delay, we can completely characterize the filter performance via a probabilistic approach. We assume the estimator maintains a buffer of length D so that at each time k, the estimator is able to retrieve all available data packets up to time k â D + 1. Both the cases of sensor with and without necessary computation capability for filter updates are considered. When the sensor has no computation capability, for a given D, we give lower and upper bounds on the probability for which the estimation error covariance is within a prescribed bound. When the sensor has computation capability, we show that the previously derived lower and upper bounds are equal to each other. An approach for determining the minimum buffer length for a required performance in probability is given and an evaluation on the number of expected filter updates is provided. Examples are provided to demonstrate the theory developed in the paper.  +
In this paper we describe the response of a Kinetic Monte Carlo model to time-varying growth conditions. We vary temperature and partial pressure sinusoidally and identify behavior typical of low-dimensional nonlinear systems. In particular, the frequency content of the roughness response is sensitive to the presence of steps in the surface.  +
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We describe the interaction of a rigid body and its incompressible fluid environment with reduced Euler-Lagrange equations on the appropriate Cartesian product manifold. We propose a modification to the planar form of these equations to accomodate control inputs consistent with a model for carangiform swimming. Initial Lie algebraic analysis of the resulting control system suggests its usefulness in predicting efficacious gaits for piscimimetic robots.  +
Realizing homeostatic control of metabolites or proteins is one of the key goals of synthetic circuits. However, if control is only implemented internally in individual cells, cell-cell heterogeneity may break the homeostasis on population level since cells do not contribute equally to the production or regulation. New control structures are needed to achieve robust functionality in heterogeneous cell populations. Quorum sensing (QS) serves as a collective mechanism by releasing and sensing small and diffusible signaling molecules for group decision-making. We propose a layered feedback control structure that includes a global controller using quorum sensing and a local controller via internal signal-receptor systems. We demonstrate with modeling and simulation that the global controller drives contributing cells to compensate for disturbances while the local controller governs the fail-mode performance in non-contributing cells. The layered controller can tolerate a higher portion of non-contributing cells or longer generations of mutant cells while maintaining metabolites or proteins level within a small error range, compared with only internal feedback control. We further discuss the potential of such layered structures in robust control of cell population size, population fraction and other population-dependent functions.  +
Specifications for complex engineering systems are typically decomposed into specifications for individual subsystems in a manner that ensures they are implementable and simpler to develop further. We describe a method to algorithmically construct component specifications that implement a given specification when assembled. By eliminating variables that are irrelevant to realizability of each component, we simplify the specifications and reduce the amount of information necessary for operation. We parametrize the information flow between components by introducing parameters that select whether each variable is visible to a component or not. The decomposition algorithm identifies which variables can be hidden while pre- serving realizability and ensuring correct composition, and these are eliminated from component specifications by quantification and conversion of binary decision diagrams to formulas. The resulting specifications describe component viewpoints with full information with respect to the remaining variables, which is essential for tractable algorithmic synthesis of implementations. The specifications are written in TLA+, with liveness properties restricted to an implication of conjoined recurrence properties, known as GR(1). We define an operator for forming open systems from closed systems, based on a variant of the “while-plus” operator. This operator simplifies the writing of specifications that are realizable without being vacuous. To convert the generated specifications from binary decision diagrams to readable formulas over integer variables, we symbolically solve a minimal covering problem. We show with examples how the method can be applied to obtain contracts that formalize the hierarchical structure of system design.  +
The problem of bootstrapping consists in designing agents that can learn from scratch the model of their sensori- motor cascade (the series of robot actuators, the external world, and the robot sensors) and use it to achieve useful tasks. In principle, we would want to design agents that can work for any robot dynamics and any robot sensor(s). One of the difficulties of this problem is the fact that the observations are very high dimensional, the dynamics is nonlinear, and there is a wide range of "representation nuisances" to which we would want the agent to be robust. In this paper, we model the dynamics of sensorimotor cascades using diffeomorphisms of the sensel space. We show that this model captures the dynamics of camera and range-finder data, that it can be used for long-term predictions, and that it can capture nonlinear phenomena such as a limited field of view. Moreover, by analyzing the learned diffeomorphisms it is possible to recover the "linear structure" of the dynamics in a manner which is independent of the commands representation.  +
In this work, we propose a robust network-in-the-loop control system for autonomous navigation and landing of an Unmanned-Aerial-Vehicle (UAV). To estimate the UAV's absolute pose, we develop a deep neural network (DNN) architecture for visual-inertial odometry, which provides a robust alternative to traditional methods. We first evaluate the accuracy of the estimation by comparing the prediction of our model to traditional visual-inertial approaches on the publicly available EuRoC MAV dataset. The results indicate a clear improvement in the accuracy of the pose estimation up to 25% over the baseline. Finally, we integrate the data-driven estimator in the closed-loop flight control system of Airsim, a simulator available as a plugin for Unreal Engine, and we provide simulation results for autonomous navigation and landing.  +
We propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. The proposed approach decomposes the original set of constraints into smaller subsets, and uses learning algorithms to propose sequences of abstractions that take the form of conjunctions of classifiers. The core procedure is a refinement loop that keeps improving the learned results based on counterexamples that are obtained from partial constraints that are easy to solve. Experiments show that the proposed techniques significantly improve the performance of state-of-the-art constraint solvers on many challenging benchmarks. The mechanism is capable of producing intermediate symbolic abstractions that are also important for many applications and for understanding the internal structures of hard constraint solving problems.  +
A community of genetically heterogeneous cells embedded in an unmixed medium allows for sophisticated operations by retaining spatial differentiation and coordinating division-of-labor. To establish the principles of engineering reliable cell-cell communication in a heterogeneous environment, we examined how circuit parameters and spatial placement affect the range of length and time scales over which simple communication circuits interact. We constructed several "sender" and "receiver" strains with quorum-sensing signaling circuits. The sender cell colony produces acyl homoserine lactones (AHL), which diffuse across the semisolid medium. The receiver cell colony detects these signal molecules and reports by fluorescence. We have found that a single colony of one sender variant is sufficient to induce receiver response at more than 1.5cm separation. Furthermore, AHL degradase expression in receiver colonies produces a signal threshold effect and reduces the response level in subsequent receiver colonies. Finally, our investigation on the spatial placement of colonies gave rise to the design of a multicellular long-range communication array consisting of two alternating colony types. Its signal response successfully propagated colony-by-colony along a six-colony array spanning 4.8cm at a transmission velocity of 12.8 hours per colony or 0.075cm per hour. In addition, we have developed a reaction-diffusion model that recreates the observed behaviors of the many performed experiments using data-informed parameter estimates of signal diffusion, gene expression, and nutrient consumption. These results demonstrate that a mixed community of colonies can enable new patterning programs, and the corresponding model will facilitate the rational design of complex communication networks.  +
In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models.  +
When autonomous robots interact with humans, such as during autonomous driving, explicit safety guarantees are crucial in order to avoid potentially life-threatening accidents. Many data-driven methods have explored learning probabilistic bounds over human agents' trajectories (i.e. confidence tubes that contain trajectories with probability ), which can then be used to guarantee safety with probability . However, almost all existing works consider . The purpose of this paper is to argue that (1) in safety-critical applications, it is necessary to provide safety guarantees with , and (2) current learning-based methods are ill-equipped to compute accurate confidence bounds at such low . Using human driving data (from the highD dataset), as well as synthetically generated data, we show that current uncertainty models use inaccurate distributional assumptions to describe human behavior and/or require infeasible amounts of data to accurately learn confidence bounds for . These two issues result in unreliable confidence bounds, which can have dangerous implications if deployed on safety-critical systems.  +
This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems.  +
This paper explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the behavior of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems.  +
Accelerating the pace of synthetic biology experiments requires new approaches for rapid prototyping of circuits from individual DNA regulatory elements. However, current testing standards require days to weeks due to cloning and in vivo transformation. In this work, we first characterized methods to protect linear DNA strands from exonuclease degradation in an Escherichia coli based transcription-translation cell-free system (TX-TL), as well as mechanisms of degradation. This enables the use of linear DNA PCR products in TX-TL. We then explored methods to calibrate linear DNA to plasmid DNA by concentration. We also demonstrated assembly technology to rapidly build circuits entirely in vitro from separate parts. Using this strategy, we prototyped a four-piece genetic switch in under 8 hours entirely in vitro. Rapid in vitro assembly has applications for prototyping circuits of unlimited size when combined with predictive computational models.  +
We consider identifiability of linear systems driven by white noise using a combination of distributional and time series measurements. Specifically, we assume that the system has no control inputs available and can only be observed at stationarity. The user is able to measure the full stationary state distribution as well as observe time correlations for small subsets of the state. We formulate theoretical conditions on identifiability of parameters from distributional information alone. We then give a sufficient condition and an effective necessary condition for identifiability using a combination of distributional and time series measurements. We illustrate the ideas with some simple examples as well as a biologically inspired example of a transcription and degradation process.  +
Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers.  +
A synthetic cell-cell signaling circuit should ideally be (1) metabolically lightweight, (2) insulated from endogenous gene networks, and (3) excitable rather than oscillatory or bistable. To accomplish these three features, we propose a synchronized pulse-generating circuit based on the design of published synchronized oscillators. This communication module employs a pulse generator built using Lux-type quorum sensing components and an IFFL transcriptional circuit. Both the input and output of this module are AHLs, the quorum sensing signaling molecule. Cells bearing this module therefore act as an excitable medium, producing a pulse of AHL when stimulated by exogenous AHL. Using simulation and microscopy, we demonstrate how this circuit enables traveling pulses of AHL production through microcolonies growing in two dimensions. Traveling pulses achieve cell-cell communication at longer distances than can be achieved by diffusion of signal from sender to receiver cells and may permit more sophisticated coordination in synthetic consortia.  +
This paper explores low observability flight path planning of unmanned air vehicles (UAVs) in the presence of radar detection systems. The probability of detection model of an aircraft near an enemy radar depends on aircraft attitude, range, and configuration. A detection model is coupled with a simplified aircraft dynamics model. The Nonlinear Trajectory Generation (NTG) software package developed at Caltech is used. The NTG algorithm is a gradient descent optimization method that combines three technologies: Bsplines, output space collocation and nonlinear optimization tools. Implementations are formulated with temporal constraints that allow periods of high observability interspersed with periods of low observability. Illustrative examples of optimized routes for low observability are presented.  +
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The Caltech Multi-Vehicle Wireless Testbed is an experimental platform for validating theoretical advances in multiple-vehicle coordination and cooperation, real-time networked control system, and distributed computation. This paper describes the design and development of an additional fleet of 12 second-generation vehicles. These vehicles are hovercrafts and designed to have lower mass and friction as well as smaller size than the first generation vehicles. These hovercrafts combined with the outdoor wireless testbed provide a perfect hardware platform for RoboFlag competition.  +
Traditional feedback control systems give little attention to issues associated with the flow of information through the feedback loop. Typically implemented with dedicated communication links that deliver nearly precise, reliable, and non-delayed information, researchers have not needed to concern themselves with issues related to quantized, delayed, and even lost information. With the advent of newer technologies and application areas that pass information through non-reliable networks, these issues cannot be ignored. In recent years the field of Networked Control Systems (NCS) has emerged to describe situations where these issues are present. The research in this field focuses on quantifying performance degradations in the presence of network effects and proposing algorithms for managing the information flow to counter those negative effects. In this thesis I propose and analyze algorithms for managing information flow for several Networked Control Systems scenarios: state estimation with lossy measurement signals, using input buffers to reduce the frequency of communication with a remote plant, and performing state estimation when control signals are transmitted to a remote plant via a lossy communication link with no acknowledgement signal at the estimator. Multi-agent coordinated control systems serve as a prime example of an emerging area of feedback control systems that utilize feedback loops with information passed through possibly imperfect communication networks. In these systems, agents use a communication network to exchange information in order to achieve a desired global ob jective. Hence, managing the information flow has a direct impact on the performance of the system. I also explore this area by focusing on the problem of multi-agent average consensus. I propose an algorithm based on a hierarchical decomposition of the communication topology to speed up the time to convergence. For all these topics I focus on designing intuitive algorithms that intelligently manage the information flow and provide analysis and simulations to illustrate their effectiveness.  
We present a mathematical programming-based method for model predictive control of cyber-physical systems subject to signal temporal logic (STL) specifications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of a receding horizon control framework. We prove correctness of our algorithms, and present experimental results for controller synthesis for building energy and climate control.  +
The focus of this paper is on modeling and control of Smart Thermal Grids (STGs) in which the uncertainties in the demand and/or supply are included. We solve the corre- sponding robust model predictive control (MPC) optimization problem using mixed-integer-linear programming techniques to provide a day-ahead prediction for the heat production in the grid. In an example, we compare the robust MPC approach with the robust optimal control approach, in which the day-ahead production plan is obtained by optimizing the objective function for entire day at once. There, we show that the robust MPC approach successfully keeps the supply-demand balance in the STG while satisfying the constraints of the production units in the presence of uncertainties in the heat demand. Moreover, we see that despite the longer computation time, the performance of the robust MPC controller is considerably better than the one of the robust optimal controller.  +
A generalized model predictive control (MPC) formulation is derived that extends the existing theory to a multi-vehicle formation stabilization problem. The vehicles are individually governed by nonlinear and constrained dynamics. The extension considers formation stabilization to a set of permissible equilibria, rather than a unique equilibrium. Simulations for three vehicle formations with input constrained dynamics on con¯guration space SE(2) are performed using a nonlinear trajectory generation (NTG) software package developed at Caltech. Preliminary results and an outline of future work for scaling/decentralizing the MPC approach and applying it to an emerging experimental testbed are given.  +
Model predictive control (MPC) is applied to the Caltech ducted fan, a thrust-vectored flight experiment. A real-time trajectory generation software based on spline theory and sequential quadratic programming is used to implement the MPC controllers. Timing issues related to the computation and implementation of repeatedly updated optimal trajectories are discussed. Results show computational speeds greater than 10 Hz, 2.5 times that of the actuator dynamics. The MPC controllers successfully stabilize a step disturbance applied to the ducted fan and compare favorably to LQR methods.  +
We present a mathematical programming-based method for model predictive control of discrete-time cyber- physical systems subject to signal temporal logic (STL) speci- fications. We describe the use of STL to specify a wide range of properties of these systems, including safety, response and bounded liveness. For synthesis, we encode STL specifications as mixed integer-linear constraints on the system variables in the optimization problem at each step of model predictive control. We present experimental results for controller synthesis on simplified models of a smart micro-grid and HVAC system.  +
We present a Python-based software package to automatically obtain phenomenological models of input-controlled synthetic biological circuits that guide the design using chemical reaction-level descriptive models. From the parts and mechanism description of a synthetic biological circuit, it is easy to obtain a chemical reaction model of the circuit under the assumptions of mass-action kinetics using various existing tools. However, using these models to guide design decisions during an experiment is difficult due to a large number of reaction rate parameters and species in the model. Hence, phenomenological models are often developed that describe the effective relationships among the circuit inputs, outputs, and only the key states and parameters. In this paper, we present an algorithm to obtain these phenomenological models in an automated manner using a Python package for circuits with inputs that control the desired outputs. This model reduction approach combines the common assumptions of time-scale separation, conservation laws, and species’ abundance to obtain the reduced models that can be used for design of synthetic biological circuits. We consider an example of a simple gene expression circuit and another example of a layered genetic feedback control circuit to demonstrate the use of the model reduction procedure.  +
A master equation describes the continuous-time evolution of a probability distribution, and is characterized by a simple bilinear structure and an often-high dimension. We develop a model reduction approach in which the number of possible confiurations and corresponding dimension is reduced, by removing improbable configurations and grouping similar ones. Error bounds for the reduction are derived based on a minimum and maximum time scale of interest. An analogous linear identification procedure is then presented, which computes the state and output matrices for a predetermined configuration set. These ideas are demonstrated first in a finite-dimensional model inspired by problems in surface evolution, and then in an infinite- dimensional film growth master equation.  +
We present a framework for applying the method of Proper Orthogonal Decomposition (POD) and Galerkin projection to compressible fluids. For incompressible flows, only the kinematic variables are important, and the techniques are well known. In a compressible flow, both the kinematic and thermodynamic variables are dynamically important, and must be included in the configuration space. We introduce an energy-based inner product which may be used to obtain POD modes for this configuration space. We then obtain an approximate version of the Navier-Stokes equations, valid for cold flows at moderate Mach number, and project these equations onto a POD basis. The resulting equations of motion are quadratic, and are much simpler than projections of the full compressible Navier-Stokes equations.  +
<p>This paper describes a technique for performing model reduction of systems with travelling wave solutions via a Karhunen Loeve framework.  +
Paradoxical signaling occurs when the same sig- naling molecule can trigger antagonistic cell functions. For example, T-Cells secret cytokine IL-2 which promotes T-Cell proliferation and also affects cell death. It has been shown that cells with this signaling capability have bi-stable population dynamics and can achieve identical levels of population homeostasis independent of initial cell concentrations. These capabilities are desirable in the context of synthetic population control circuits designed for application in therapeutic treatment of various diseases. It thus becomes important to understand the dependence of the cell system on the intracellular paradoxical components and to develop accurate models to provide insight into optimal design characteristics. Here, we create a model that integrates three IL-2 driven intracellular mechanisms that trigger 1) T-cell proliferation 2) T-cell apoptosis and 3) IL-2 production. Using this model, we are able to explore the internal mechanisms necessary for paradoxical signaling in T-Cells. It was shown that the intracellular mechanisms considered were sufficient to produce population dynamic characteristics of paradoxical signaling consistent with published systems level models and data. Furthermore, analysis of parameters revealed dependency of population homeostatic stability on the production and activation of the specific intracellular proteins considered.  +
The problem of model reduction of linear systems with certain interconnection structure is considered in this paper. To preserve the interconnection structure between subsystems in the reduction, special care needs to be taken. This problem is important and timely because of the recent focus on complex networked systems in control engineering. Two different model-reduction methods are introduced and compared in the paper. Both methods are extensions to the well-known balanced truncation method. Compared to earlier work in the area these methods use a more general linear fractional transformation framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that reduce to classical bounds in special cases are derived. So-called structured Hankel singular values  +
An experimental investigation of acoustic mode noise suppression was conducted in a cavity using a digital controller with a linear control algorithm. The control algorithm was based on flow field physics similar to the Rossiter model for acoustic resonance. Details of the controller and results from its implementation are presented in the companion paper by Rowley, et al (2002). Here the experiments and some details of the flow field development are described, which were done primarily at Mach number 0.34 corresponding to single mode resonance in the cavity. A novel method using feedback control to suppress the resonant mode and open-loop forcing to inject a non-resonant mode was developed for system identification. The results were used to obtain empirical transfer functions of the components of resonance, and measurements of the shear layer growth for use in the design of the control algorithm.  +
Experiments using active control to reduce oscillations in the flow past a rectangular cavity have uncovered surprising phenomena: in the controlled system, often new frequencies of oscillation appear, and often the main frequency of oscillation is split into two sideband frequencies. The goal of this paper is to explain these effects using physics-based models, and to use these ideas to guide control design. We present a linear model for the cavity flow, based on the physical mechanisms of the familiar Rossiter model. Experimental data indicates that under many operating conditions, the oscillations are not self-sustained, but in fact are caused by amplification of external disturbances. We present some experimental results demonstrating the peak-splitting phenomena mentioned above, use the physics-based model to study the phenomena, and discuss fundamental performance limitations which limit the achievable performance of any control scheme.  +
This paper applies some previously studied extended Kalman filter techniques for planar road geometry estimation to the domain of autonomous navigation of offhighway vehicles. In this work, a clothoid model of the road geometry is constructed and estimated recursively based on road features extracted from single-axis LADAR range measurements. We present a method for feature extraction of the road centerline in the image plane, and describe its application to recursive estimation of the road geometry. We analyze the performance of our method against simulated motion of varied road geometries and against recorded data from previous autonomous navigation runs. Our method accomodates full 6 DOF motion of the vehicle as it navigates, constructs consistent estimates of the road geometry with respect to a fixed global reference frame, and requires an estimate of the sensor pose for each range measurement.  +
Targeted transcriptional repression with catalytically inactive Cas9 (CRISPRi) can be used to build gene regulatory nets similar in principle to those made with traditional transcription factors, and promises to do so with better orthogonality, programmability, and extensibility. We use a simple dynamical model of CRISPRi to understand its behavior and requirements, and to show that CRISPRi can recapitulate several classic gene regulatory circuits, including the repressilator, a toggle switch, and an incoherent feed-forward loop pulse generator. Our model also predicts that these circuits are highly sensitive to promoter leak, but that promoter leak can be offset with active degradation of dCas. We provide specifications for required fold-repression and dCas degradation rates for several dynamic circuits. Our modeling reveals key engineering requirements and considerations for the construction of dynamic CRISPRi circuits, and provides a roadmap for building those circuits.  +
In this paper we consider the problem of repre- senting a biological system and its environment using a stochas- tic modeling framework. We first introduce a decomposition of the global chemical reaction system into two systems: a system of interest and its environment. We then present and derive a decomposition of the chemical master equation to achieve a representation describing the dynamics of the system of inter- est, perturbed by an environmental disturbance. We use this decomposition to model examples of two types of environmental disturbances: the disturbance a system experiences through loading effects from limited resources and the disturbance a system experiences when perturbed by an antibiotic that modifies transcription or translation rates.  +
Thin film deposition is a manufacturing process in which tolerances may approach the size of individual atoms. The final film is highly sensitive to the processing conditions, which can be intentionally manipulated to control film properties. A lattice model of surface evolution during thin film growth captures many important features, including the nucleation and growth of clusters of atoms and the propagation of atomic-height steps. The dimension of this probabilistic master equation is too large to directly simulate for any physically realistic domain, and instead stochastic realizations of the lattice model are obtained with kinetic Monte Carlo simulations. <p> In this thesis simpler representations of the master equation are developed for use in analysis and control. The static map between macroscopic process conditions and microscopic transition rates is first analyzed. In the limit of fast periodic process parameters, the surface responds only to the mean transition rates, and, since the map between process parameters and transition rates is nonlinear, new effective combinations of transition rates may be generated. These effective rates are the convex hull of the set of instantaneous rates. <p> The map between transition rates and expected film properties is also studied. The dimension of a master equation can be reduced by eliminating or grouping configurations, yielding a reduced-order master equation that approximates the original one. A linear method for identifying the coefficients in a master equation is then developed, using only simulation data. These concepts are extended to generate low-order master equations that approximate the dynamic behavior seen in large Monte Carlo simulations. The models are then used to compute optimal time-varying process parameters. <p> The thesis concludes with an experimental and modeling study of germanium film growth, using molecular beam epitaxy and reflection high-energy electron diffraction. Growth under continuous and pulsed flux is compared in experiment, and physical parameters for the lattice model are extracted. The pulsing accessible in the experiment does not trigger a change in growth mode, which is consistent with the Monte Carlo simulations. The simulations are then used to suggest other growth strategies to produce rougher or smoother surfaces.  
Thin film deposition is an industrially-important process to which control theory has not historically been applied. The need for control is growing as the size of integrated circuits shrinks, requiring increasingly tighter tolerances in the manufacture of thin films. Our contributions in this study are two-fold: we formulate a model of thin film growth as a control system and we examine the effects of fast periodic forcing. <p> We choose a lattice formulation of crystal growth as our physical model, which captures atomic length scale effects at a time scale compatible with film growth. We focus on the control of film morphology, or surface height profile. Although the system dimension is high, the structure is simple: the dynamics and the output are linear in the state. We consider the process conditions as inputs, which alter the transition rate functions. In the evolution equation, each of these nonlinear functions is multiplied by a linear vector field, yielding a system with a structure similar to a bilinear system. <p> The process conditions in some deposition methods are inherently unsteady, which produces films with altered morphology. We use the model developed in this study to analyze the effects of fast periodic forcing on thin film evolution. With the method of averaging we develop new effective transition rates which may produce film properties unattainable with constant inputs. We show that these effective rates are the convex hull of the set of rates associated with constant inputs. We present conditions on the convex hull for which the finite-time and infinite-time reachability sets cannot be expanded with fast periodic forcing. An example in which this forcing increases the reachability set and produces more desirable morphology is also presented.  +
Synthetic transcriptional networks built from CRISPR-based repressors (CRISPRi) rely on shared use of a core dCas9 protein. In E. coli, CRISPRi cannot support more than about a dozen simultaneous gRNAs before the fold repression of any individual gRNA drops below 10x. We show with a simple model based on previous characterization of competition in CRISPRi that activation by CRISPR-based activators (CRISPRa) is much less sensitive to dCas9 bottle-necking than CRISPRi. We predict that E. coli should be able to support dozens to hundreds of CRISPRa gRNAs at >10-fold activation.  +
One of the fundamental challenges in synthesizing complex biocircuits from existing biocircuit components is understanding how the spatial arrangement of biocircuit components impacts component behavior. In this paper we develop a set of synthetic biology parts for systematically probing the effects of spatial arrangement on transcriptional expression. Our initial experimental assays prove that even the rearrangement of two biocircuit parts (comprised of a promoter, coding sequence, and terminator) into three spatially distinct orientations (convergent, divergent, and tandem orientation) can exhibit significantly different levels of transcriptions. These findings motivate the need for mathematical models to describe these spatial context effects. We pose a novel nonlinear mass-action kinetics based model that enables the integration of knowledge about spatial or compositional context and canonical descriptions of transcriptional dynamics. Our findings suggest that compositional context is a key factor in determining bio- circuit part performance and thus represent another important piece in biocircuit interconnection theory.  +
We propose a planar model for the swimming of certain marine animals based on reduced Euler-Lagrange equations for the interaction of a rigid body and an incompressible fluid. This model assumes the form of a control-affine nonlinear system with drift; preliminary accessibility analysis suggests its utility in predicting efficacious gaits for piscimimetic robots. We account for the generation of thrust due to vortex shedding through controlled coupling terms. At the heart of this coupling is an abstraction from hydrofoil theory; we investigate its applicability to real swimming using an articulated robotic caudal fin. We compare the observed behavior of our experimental apparatus to that predicted numerically by steady hydrodynamic theory.  +
We propose a model for planar carangiform swimming based on conservative equations for the interaction of a rigid body and an incompressible fluid. We account for the generation of thrust due to vortex shedding through controlled coupling terms. We investigate the correct form of this coupling experimentally with a robotic propulsor, comparing its observed behavior with that predicted by unsteady hydrodynamics. Our analysis of thrust generation by an oscillating hydrofoil allows us to characterize and evaluate certain families of gaits. Our final swimming model takes the form of a control-affine nonlinear system.  +
This work discusses feasibility aspects of motion planning for groups of agents connected by a range-constrained wireless network. Specifically, we address the difficulties encountered when trajectories are required to preserve the connectedness of the network. The analysis utilizes a quantity called the connectivity robustness of the network, which can be calculated in a distributed fashion, and thus is applicable to distributed motion planning problems arising in control of vehicle networks. Further, these results show that network constraints posed as connectivity robustness constraints have minimal impact on reachability, provided that an appropriate topology control algorithm is implemented. This contrasts with more naive approaches to connectivity maintenance, which can significantly reduce the reachable set.  +
We consider the problem of planning motions in observations space, based on learned models of the dynamics that associate to each action a diffeomorphism of the observations domain. For an arbitrary set of diffeomorphisms, this problem must be formulated as a generic search problem. We adapt established algorithms of the graph search family. In this scenario, node expansion is very costly, as each node in the graph is associated to an uncertain diffeomorphism and corresponding predicted observations. We describe several improvements that ameliorate performance: the introduction of better image similarities to use as heuristics; a method to reduce the number of expanded nodes by preliminarily identifying redundant plans; and a method to pre-compute composite actions that make the search efficient in all directions.  +
While the use of formal synthesis for robotics problems in which the environment may act adversarially provides for exactârather than probabilisticâcorrectness of controllers, such methods are impractical when the adversary can move freely in a large portion of the workspace. As is well-known, this is due to exponential growth in the state space with the addition of each new problem variable. Furthermore, such an approach is overly conservative because most configurations will not be reached in typical runs. Rather than entirely abandon the discrete game view, we propose a combined method that ensures exact satisfaction of a given specification, expressed in linear temporal logic, while providing a lower bound on robot-obstacle distance throughout execution. Our method avoids explicit encoding of the moving obstacle and thus substantially reduces the reactive synthesis problem size, while allowing other nondeterministic variables to still be included in the specification. Our approaches centers on modeling obstacle motion as changes in the presence of a virtual static obstacle, and performing incremental synthesis in response. The algorithm is tested in application to a planar surveillance task.  +
Consensus protocols in coordinated multi-agent systems are distributed algorithms. Just using local information available to each single agent, all agents converge to an identical consensus state and the convergence speed is determined by the algebraic connectivity of the communication network. In order to achieve a faster consensus seeking, we propose multi-hop relay protocols based on the current ``nearest neighbor rules'' consensus protocols. By employing multiple-hop paths in the network, more information is passed around and each agent enlarges its "available" neighborhood. We demonstrate that these relay protocols can increase the algebraic connectivity without physically adding or changing any communication links. Moreover, time delay sensitivity of relay protocols are discussed in detail. We point out that a trade off exists between convergence performance and time delay robustness. Simulation results are also provided to verify the efficiency of relay protocols.  +
We consider the estimation of a vector state based on m measurements that can be potentially manipulated by an adversary. The attacker is assumed to have limited resources and can only manipulate up to l of the m measurements. However, it can the compromise measurements arbitrarily. The problem is formulated as a minimax optimization, where one seeks to construct an optimal estimator that minimizes the âworst-caseâ error against all possible manipulations by the attacker and all possible sensor noises. We show that if the system is not observable after removing 2l sensors, then the worst-case error is infinite, regardless of the estimation strategy. If the system remains observable after removing arbitrary set of 2l sensor, we prove that the optimal state estimation can be computed by solving a semidefinite programming problem. A numerical example is provided to illustrate the effectiveness of the proposed state estimator.  +
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Temporal dynamics in many biomolecular circuits can change with temperature because of the temperature dependence of underlying reaction rate parameters. It is generally unclear what circuit mechanisms can inherently facilitate robustness in the dynamics to variations in temperature. Here, we address this issue using a combination of mathematical models and experimental measure- ments in a cell-free transcription-translation system. We find that negative transcriptional feedback can reduce the eâµect of temperature variation on circuit dynamics. Further, we find that effective negative feedback due to first-order degradation mechanisms can also enable such a temperature robustness effect. Finally, we estimate temperature dependence of key parameters mediating such negative feedback mechanisms. These results should be useful in the design of temperature robust circuit dynamics.  +
We propose a negative feedback architecture that regulates activity of artificial genes, or "genelets", to meet their output downstream demand, achieving robustness with respect to uncertain open-loop output production rates. In particular, we consider the case where the outputs of two genelets interact to form a single assembled product. We show with analysis and experiments that negative autoregulation matches the production and demand of the outputs: the magnitude of the regulatory signal is proportional to the error between the circuit output concentration and its actual demand. This two-device system is experimentally implemented using in vitro transcriptional networks, where reactions are systematically designed by optimizing nucleic acid sequences with publicly available software packages. We build a predictive ordinary differential equation (ODE) model that captures the dynamics of the system, and can be used to numerically assess the scalability of this architecture to larger sets of interconnected genes. Finally, with numerical simulations we contrast our negative autoregulation scheme with a cross-activation architecture, which is less scalable and results in slower response times.  +
We describe the structure of the graphs with the smallest average distance and the largest average clustering given their order and size. There is usually a unique graph with the largest average clustering, which at the same time has the smallest possible average distance. In contrast, there are many graphs with the same minimum average distance, ignoring their average clustering. The form of these graphs is shown with analytical arguments. Finally, we measure the sensitivity to rewiring of this architecture with respect to the clustering coefficient, and we devise a method to make these networks more robust with respect to vertex removal.  +
In this paper we provide new design principles for estimation over wireless fading channels in mobile sensor networks. We show how to optimize receiver and transmitter designs to improve estimation performance in the application layer. On the receiver side, we show that the optimum packet drop mechanism is the one that provides a balance between information loss and communication noise. On the transmitter side, we show how to optimize and adapt the transmission rate for performance improvement in the application layer. We further provide stability conditions for different design strategies. The work confirms that delay-sensitive mobile sensor applications require new design paradigms and applying the same design principles of data networks can lead to performance degradation. The work also highlights the importance of cross-layer feedback and provides alternative designs if such feedbacks are not available.  +
<h3>Abstract</h3> This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the point of view of Lagrangian mechanics and with a view to control theoretical applications. The basic methodology is that of geometric mechanics emphasizing the formulation of Lagrange d'Alembert with the use of connections and momentum maps associated with the given symmetry group. We begin by recalling and extending the results of Koiller from the case of principal connections to the general Ehresmann case. Unlike the situation with standard configuration space constraints, the symmetry in the nonholonomic case may or may not lead to conservation laws. In any case, the momentum map determined by the symmetry group satisfies a useful differential equation that decouples from the group variables. This momentum equation is shown to have the form of a covariant derivative of the momentum equal to a component of the internal generalized force. An alternative description using a "body reference frame" realizes part of the momentum equation as those components of the Euler-Poincare equations along the symmetry directions consistent with the constraints. One of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not. An example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard, a modified version of the skateboard which uses momentum coupling for locomotion generation. We construct a synthesis of the mechanical connection and the Ehresmann connection defining the constraints, obtaining an important new object, the nonholonomic connection. Under conditions that include the Chaplygin case (we use the terminology "purely kinematic") and the case in which the momentum is conserved, it is known that one can perform a reduction similar to Lagrangian reduction, which includes the Routh procedure. We generalize this reduction procedure to the case in which the nonholonomic connection is a principal connection for the given symmetry group; this case includes all of the examples considered in the paper and many others as well, such as the wobblestone, the nonvertical disk and the bicycle. Another purpose of this work is to lay the foundation for future work on mechanical systems with control so that one can adapt well developed techniques from holonomic systems, such as constructive controllability and geometric phases. Although this will be the subject of future work, the methodology of the present paper is developed with these goals in mind.  
This work develops the geometry and dynamics of mechanical systems with nonholonomic constraints and symmetry from the perspective of Lagrangian mechanics and with a view to control theoretical applications. The basic methodology is that of geometric mechanics applied to the formulation of Lagrange d'Alembert, generalizing the use of connections and momentum maps associated with a given symmetry group to this case. We begin by formulating the mechanics of nonholonomic systems using an Ehresmann connection to model the constraints, and show how the curvature of this connection enters into Lagrange's equations. Unlike the situation with standard configuration space constraints, the presence of symmetries in the nonholonomic case may or may not lead to conservation laws. However, the momentum map determined by the symmetry group still satisfies a useful differential equation that decouples from the group variables. This momentum equation, which plays an important role in control problems, involves parallel transport operators and is computed explicitly in coordinates. An alternative description using a ``body reference frame'' relates part of the momentum equation to the components of the Euler-Poincar\'{e} equations along those symmetry directions consistent with the constraints. One of the purposes of this paper is to derive this evolution equation for the momentum and to distinguish geometrically and mechanically the cases where it is conserved and those where it is not. An example of the former is a ball or vertical disk rolling on a flat plane and an example of the latter is the snakeboard, a modified version of the skateboard which uses momentum coupling for locomotion generation. We construct a synthesis of the mechanical connection and the Ehresmann connection defining the constraints, obtaining an important new object we call the nonholonomic connection. When the nonholonomic connection is a principal connection for the given symmetry group, we show how to perform Lagrangian reduction in the presence of nonholonomic constraints, generalizing previous results which only held in special cases. Several detailed examples are given to illustrate the theory.  
Analysis and simulations are performed for a simplified model of a commercially available variant on the skateboard, known as the Snakeboard. Although the model exhibits basic gait patterns seen in a large number of locomotion problems, the analysis tools currently available do not apply to this problem. The difficulty is seen to lie primarily in the way in which the nonholonomic constraints enter into the system. As a first step towards understanding systems represented by our model we present the equations of motion and perform some controllability analysis for the snakeboard. We also perform some numerical simulations of the gait patterns.  +
In this paper we investigate methods for steering systems with nonholonomic constraints between arbitrary configurations. Early work by Brockett derives the optimal controls for a set of canonical systems in which the tangent space to the configuration manifold is spanned by the input vector fields and their first order Lie brackets. Using Brockett's result as motivation, we derive suboptimal trajectories for systems which are not in canonical form and consider systems in which it takes more than one level of bracketing to achieve controllability. These trajectories use sinusoids at integrally related frequencies to achieve motion at a given bracketing level. We define a class of systems which can be steered using sinusoids (chained systems) and give conditions under which a class of two-input systems can be converted into this form.  +
In this paper we present a control law for globally asymptotically stabilizing a class of controllable nonlinear systems without drift. The control law converts into closed loop feedback earlier strategies for open loop steering of nonholonomic systems using sinusoids at integrally related frequencies. The global result is obtained by introducing saturation functions. Simulation results for stabilizing a simple kinematic model of an automobile are included.  +
Rotating stall and surge are aerodynamic instabilities that limit the performance of aeroengines. A set of magnetic bearings supporting the compressor rotor is a potential actuator for active control of rotating stall and surge. Based on a first-principles model we show that using this type of actuation, the first harmonic mode of rotating stall is linearly controllable, but the second harmonic mode and the surge mode are linearly uncontrollable. We then give an explicit procedure for designing feedback laws such that the first mode is linearly stabilized and the criticality of the Hopf bifurcations of the second mode and the surge mode are supercritical. We also investigate the effects of magnitude saturation on the regions of attraction. We demonstrate the theoretical results by numerical simulations of a model for a transonic compressor at the NASA Lewis Research Center.  +
This paper considers the design of motion control algorithms for robot fish. We present modeling, control design, and experimental trajectory tracking results for a planar robotic fish that is propelled using the carangiform style of locomotion. Our experimental apparatus consists of a freely translating and rotating flat plate and a two-link actuated tail. We develop a model for the fish's propulsion that is based on quasi-steady fluid flow. Using this model, we predict system response to sinusoidal motions of the tail joints and compare these predictions to the experimental results. We then propose gaits for forward and turning trajectories and analyze system response under such control strategies. Our models and predictions are verified by experiment.  +
This thesis focuses on understanding the use of air injection as a means of controlling rotating stall in an axial flow compressor, involving modeling, dynamical systems analysis, and experimental investigations. <p> The first step towards this understanding was the development of a low order model for air injection control, the starting point of which was the Moore and Greitzer model for axial flow compressors. The Moore and Greitzer model was extended to include the effects of air injection and bifurcation analysis was performed to determine how the closed loop system dynamics are different from those of the open loop system. This low order model was then used to determine the optimal placement of the air injection actuators. <p> Experimental work focused on verifying that the low order model, developed for air injection actuation, qualitatively captured the behavior of the Caltech compressor rig. Open loop tests were performed to determine how the placement of the air injectors on the rig affected the performance of the compressor. The positioning of the air injectors that provided the greatest control authority were used in the development of air injection controllers for rotating stall. The controllers resulted in complete elimination of the hysteresis associated with rotating stall. The use of a throttle actuator for the control of the surge dynamics was investigated, and then combined with an air injection controller for rotating stall; the resulting controller performed quite well in throttle disturbance rejection tests. <p> A higher order model was developed to qualitatively match the experimental results with a simulation. The results of this modeling effort compared quite well with the experimental results for the open loop behavior of the Caltech rig. The details of how the air injection actuators affect the compressor flow were included in this model, and the simulation predicted the same optimal controller that was developed through experimentation. <p> The development of the higher order model also included the investigation of systematic methods for determining the simulation parameters. Based on experimental measurements of compression system transients, the open loop simulation parameters were identified, including values for the compressor performance characteristic in regions where direct measurements were not possible. These methods also provided information on parameters used in the modeling of the pressure rise delivered by the compressor under unsteady flow conditions. <p>  
Recent advances in geometric mechanics, motivated in large part by applications in control theory, have introduced new tools for understanding and utilizing the structure present in mechanical systems. In particular, the use of geometric methods for analyzing Lagrangian systems with both symmetries and non-integrable (or nonholonomic) constraints has led to a unified formulation of the dynamics that has important implications for a wide class of mechanical control systems. This paper presents a survey of recent results in this area, focusing on the relationships between geometric phases, controllability, and curvature, and the role of trajectory generation in nonlinear controller synthesis. Examples are drawn from robotics and flight control systems, with an emphasis on motion control problems.  +
Nonlinear control of mechanical systems is a challenging discipline that lies at the intersection between control theory and geometric mechanics. This thesis sheds new light on this interplay while investigating motion control problems for Lagrangian systems. Both stability and motion planning aspects are treated within a unified framework that accounts for a large class of devices such as robotic manipulators, autonomous vehicles and locomotion systems.</p> <p>One distinguishing feature of mechanical systems is the number of control forces. For systems with as many input forces as degrees of freedom, many control problems are tractable. One contribution of this thesis is a set of trajectory tracking controllers designed via the notions of configuration and velocity error. The proposed approach includes as special cases a variety of results on joint and workspace control of manipulators as well as on attitude and position control of vehicles.</p> <p>Whenever fewer input forces are available than degrees of freedom, various control questions arise. The main contribution of this thesis is the design of motion algorithms for vehicles, i.e., rigid bodies moving in Euclidean space. First, an algebraic controllability analysis characterizes the set of reachable configurations and velocities for a system starting at rest. Then, provided a certain controllability condition is satisfied, various motion algorithms are proposed to perform tasks such as short range reconfiguration and hovering. </p> <p>Finally, stabilization techniques for underactuated systems are investigated. The emphasis is on relative equilibria, i.e., steady motions for systems that have a conserved momentum. Local exponential stabilization is achieved via an appropriate splitting of the control authority.  +
Active control of rotating stall and surge using bleed valves has been demonstrated on low and high speed compressors using high bandwidth actuators. In this paper we provide a method to reduce the bandwidth and rate requirements for control of rotating stall by combining an axisymmetric bleed valve with continuous air injection. The addition of the continuous air injection is modeled as a shift of both the stable and unstable parts of the compressor characteristic and serves to reduce the requirement of a bleed valve used for rotating stall stabilization purpose. The results are demonstrated using a low-speed, single stage, axial flow compressor.  +
The study of compressor instabilities in gas turbine engines has received much attention in recent years. In particular, rotating stall and surge are major causes of problems ranging from component stress and lifespan reduction to engine explosion. In this thesis, modeling and control of rotating stall and surge using bleed valve and air injection is studied and validated on a low speed, single stage, axial compressor at Caltech. <p> Bleed valve control of stall is achieved only when the compressor characteristic is actuated, due to the fast growth rate of the stall cell compared to the rate limit of the valve. Furthermore, experimental results show that the actuator rate requirement for stall control is reduced by a factor of fourteen via compressor characteristic actuation. Analytical expressions based on low order models (2--3 states) and a high fidelity simulation (37 states) tool are developed to estimate the minimum rate requirement of a bleed valve for control of stall. A comparison of the tools to experiments show a good qualitative agreement, with increasing quantitative accuracy as the complexity of the underlying model increases. <p> Air injection control of stall and surge is also investigated. Simultaneous control of stall and surge is achieved using axisymmetric air injection. Three cases with different injector back pressure are studied. Surge control via binary air injection is achieved in all three cases. Simultaneous stall and surge control is achieved for two of the cases, but is not achieved for the lowest authority case. This is consistent with previous results for control of stall with axisymmetric air injection without a plenum attached. <p> Non--axisymmetric air injection control of stall and surge is also studied. Three existing control algorithms found in literature are modeled and analyzed. A three--state model is obtained for each algorithm. For two cases, conditions for linear stability and bifurcation criticality on control of rotating stall are derived and expressed in terms of implementation--oriented variables such as number of injectors. For the third case, bifurcation criticality conditions are not obtained due to complexity, though linear stability property is derived. A theoretical comparison between the three algorithms is made, via the use of low--order models, to investigate pros and cons of the algorithms in the context of operability. <p> The effects of static distortion on the compressor facility at Caltech is characterized experimentally. Results consistent with literature are obtained. Simulations via a high fidelity model (34 states) are also performed and show good qualitative as well as quantitative agreement to experiments. A non--axisymmetric pulsed air injection controller for stall is shown to be robust to static distortion.  
This paper proposes an intuitive nonlinear lateral control strategy for trajectory tracking in autonomous nonholonomic vehicles. The controller has been implemented and verified in Alice, Team Caltech's contribution to the 2007 DARPA Urban Challenge competition for autonomous motorcars. A kinematic model is derived. The control law is described and analyzed. Results from simulations and field tests are given and evaluated. Finally, the key features of the proposed controller are reviewed, followed by a discussion of some limitations of the proposed strategy.  +
The problem of finding a real time optimal trajectory to minimize the probability of detection (to maximize the probability of notbeingdetected, pnd, function) of unmanned air vehicles by opponent radar detection systems is investigated. This paper extends our preliminary results on low observable trajectory generation in three ways. First, trajectory planning in the presence of detection by multiple radar systems, rather than single radar systems, is considered. Second, an overall probability of detection function is developed for the multiple radar case. In previous work, both probability of detection by a single radar and signature were developed in the theory section, but the examples used only signature constraints. In this work, the use of the overall probability of detection function is used, both because it aids in the extension to multiple radar systems and because it is a more direct measure of the desirable optimization criteria. The third extension is the use of updated signature and probability of detection models. The new models have a greater number of sharp gradients than the previous models, with low detectability regions for both a cone shaped areas centered around the nose as in the previous paper, as well as a cone-shaped area centered around rear of the air vehicle. The Nonlinear Trajectory Generation method (NTG), developed at Caltech, is used and motivated by the ability to provide real time solutions for constrained nonlinear optimization problems. Numerical simulations of multiple radar scenarios illustrate UAV trajectories optimized for both detectability and time.  +
The Caltech Multi Vehicles Wireless Testbed (MVWT) is a platform designed to explore theoritical advances in multi-vehicle coordination and control, networked control systems and high con�dence distributed computation. The contribution of this report is to present simulation and experimental results on the generation and implementation of optimal trajectories for the MVWT vehicles. The vehicles are nonlinear and spatially contrained with bounded input control. The trajectories are generated using the NTG software package developed at Caltech. Minimum time trajectories and the application of Model Predictive Control (MPC) are investigated. can actually follow i.e. trajectories that satisfy every constraint of the testbed. Those constraints can either be linear, like the boundaries of the testbed or nonlinear like the constraints on the input. The main di�erence and also di�culty in our case is that the system is not linearly controllable around its equilibrium. In Section 2 we will give a quick description of the systems properties and in Section 3 and 4 we will describe the progression which led us from the optimization problem to the implementation on the real vehicles. In Section 5 other optimization problems such as minimum time trajectory generation and model predictive control are investigated.  +
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Using geometric concepts from observability theory for nonlinear systems, we propose an approach for parameter estimation for linearly and nonlinearly parameterized systems that does not rely on persistence of excitation conditions. The proposed approach relies on extending a parameter estimation problem to a state estimation problem by introducing the parameters as auxiliary state variables. Applying tools from geometric nonlinear control theory we give an observability check for parameters, and, in case the parameters are observable, we provide a constructive way to design a local parameter observer with established speed of convergence.  +
The observability properties of a class of hybrid systems whose continuous variables are available for measurement are considered. We show that the discrete variables' dynamics can be always extended for observable systems to a lattice in such a way that the extended system has the properties that allow the construction of the LU discrete state estimator. Such an estimator updates two variables at each step, namely the upper and lower bound of the set of all possible discrete variables' values compatible with the output sequence. We give an estimate of the complexity of the estimator in the worst case.  +
In this paper we consider the problem of estimating discrete variables in a class of hybrid systems where we assume that the continuous variables are available for measurement. Using lattice and order theory we develop a framework for constructing an observer on an enlarged space of variables with lattice structure, which updates only two variables at each step. We apply our ideas to a multi-robot system example, the RoboFlag Drill.  +
This paper considers how a team of mobile sensors should cooperatively move so as to optimally categorize a single moving target from their noisy sensor readings. The cooperative control procedure is based on the development of a cost function that quantifies the teamâs classification error. The robotsâ motions are then chosen to minimize this function. We particularly investigate the case where the sensor noise and class distributions are Gaussian. In this case, we can derive a duality principle which states that optimal classification will be realized when the covariance of the target estimate is minimized. That is, in this case, optimal estimation leads naturally to optimal classification. We extend previous work to develop a distributed discrete-gradient search algorithm that guides the teamâs location motions for purposes of optimal estimation and classification. The concepts developed are validated through numerical studies.  +
AbstractIn this paper, we consider the problem of optimal Linear Quadratic Gaussian control of a system in which communication between the sensor and the controller occurs across a packet-dropping link. We first prove a separation principle that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. Then we present one such optimal algorithm, which consists of a Kalman filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for any arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design.  +
Many problems in nonlinear control theory (like, for instance, feedback linearization problem) lead to examination of integrability of a Pfaffian system. In a generic case a Pfaffian system is not integrable. Therefore, how to approximate nonintegrable Pfaffian systems by integrable ones and how this approximation can be applied in practice appears to be a natural and important problem. In the present paper we establish some measures of non-integrability of Pfaffian system of arbitrary dimension and discuss their relation to approxiations of non-integrable Pfaffian systems by integrable ones. Our work is motivated by expected applications to approximate feedback linearization of multi-input nonlinear systems.  +
This paper is concerned with the distributed averaging problem subject to a quantization constraint. Given a group of agents associated with scalar numbers, it is assumed that each pair of agents can communicate with each other with a prescribed probability, and that the data being exchanged between them is quantized. In this part of the paper, it is proved that the stochastic gossip algorithm proposed in a recent paper leads to reaching the quantized consensus. Some important properties of the system in the steady-state (after reaching the consensus) are also derived. The results developed here hold true for any arbitrary quantization, provided the tuning parameter of the gossip algorithm is chosen properly. The expected value of the convergence time bounded in the second part of the paper.  +
This paper deals with the distributed averaging problem over a connected network of agents, subject to a quantization constraint. It is assumed that at each time update, only a pair of agents can update their own numbers in terms of the quantized data being exchanged. The agents are also required to communicate with one another in a stochastic fashion. In the first part of the paper, it was shown that the quantized consensus is reached by means of a stochastic gossip algorithm proposed in a recent paper, for any arbitrary quantization. The current part of the paper considers the expected value of the time at which the quantized consensus is reached. This quantity (corresponding to the worst case) is upper and lower bounded in terms of the topology of the graph, for uniform quantization. In particular, it is shown that these bounds are related to the principal minors of the weighted Laplacian matrix. A convex optimization is also proposed to determine the set of probabilities (used to pick a pair of agents) which leads to the fast convergence of the gossip algorithm.  +
We study the problem of using a small number of mobile sensors to monitor various threats in a geographical area. Using some recent results on stochastic sensor scheduling, we propose a stochastic sensor movement strategy. We present simple conditions under which it is not possible to maintain a bounded estimate error covariance for all the threats. We also study a simple sub-optimal algorithm to generate stochastic trajectories. Simulations are presented to illustrate the results.  +
In this paper we look at the problem of multi-sensor data fusion when data is being communicated over channels that drop packets randomly. We are motivated by the use of wireless links for communication among nodes in upcoming sensor networks. We wish to identify the information that should be communicated by each node to others given that some of the information it had transmitted earlier might have been lost. We solve the problem exactly for the case of two sensors and study the performance of the algorithm when more sensors are present. For the two-sensor case, the performance of our algorithm is optimal in the sense that if a packet is received from the other sensor, it is equivalent to receiving all previous measurements, irrespective of the packet drop pattern.  +
We study a simple pursuit scenario in which the pursuer has potential access to an additional off-board global sensor. However, the global sensor can be used for either of two purposes: to improve the state estimate of the pursuer, or to obtain more data about the trajectory being tracked. The problem is to determine the variation in the performance of the system as the global sensor changes its behavior. We use a stochastic strategy to optimize over the transmission pattern of the global sensor.  +
In this paper, we consider the problem of active sensing using mobile sensor nodes that are jointly estimating the state of a dynamic target as a sensor network. We propose a gradient search-based decentralized algorithm that demonstrates the benefits of distributed sensing. We then examine the task of tracking multiple targets. We use a greedy algorithm for associating sensors with targets along with the gradientsearch strategy for sensor vehicle motion planning. Simulation results show that these simple decentralized strategies perform quite well and the sensor nodes exhibit interesting cooperative behavior.  +
In this note we consider the following problem. Suppose a set of sensors is jointly trying to estimate a process. One sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors. What is the sensor schedule that results in the mininmum error covariance? We describe a stoachastic sensor selection strategy that is easy to implement and is computationally tractable. The problem described above comes up in many domains out of which we discuss two. In the sensor selection problem, there are multiple sensors that cannot operate simultaneously (eg, sonars in the same frequency band). Thus measurements need to be scheduled. In the sensor coverage problem, a geographical area needs to be covered by mobile sensors each with limited range. Thus from every position, the sensors obtain a different viewpoint of the area and the sensors need to optimize their positions. The algorithm is applied to these problems and illustrated through simple examples.  +
We analyze a jump linear Markov system being stabilized using a zero-order hold controller. We consider the case when the Markov state is associated with the probability distribution of a measured variable. We assume that the Markov state is not known, but rather is being estimated based on the observations of the variable. We present conditions for the stability of such a system and also solve the optimal LQR control problem for the case when the state estimate update uses only the last observation value. In particular we consider a suboptimal causal version of the Viterbi estimation algorithm and show that a separtion property does not hold between the optimal control and the Markov state estimate. Some simple examples are also presented.  +
We study the effect of quantization on the performance of a scalar dynamical system. We provide an expression for calculation of the LQR cost of a dynamical system for a general quantizer. Using the high-rate approximation, we evaluate it for two commonly used quantizers: uniform and logarithmic. We also provide a lower bound on performance of the optimal quantizer based on entropy arguments and consider the case when the channel drops data packets stochastically.  +
We study the synthesis problem of a LQR controller when the matrix describing the control law is additionally constrained to lie in a particular vector space. Our motivation is the use of such control laws to stabilize networks of autonomous agents in a decentralized fashion; with the information ow being dictated by the constraints of a pre-specified topology. We formulate the problem as an optimization problem and provide numerical procedures to solve it. Then we apply the technique to the decentralized vehicle formation control problem and show that the topology can have a significant effect on the optimal cost. We also discuss the issue of optimal topology.  +
Despite the significant role integral membrane proteins (IMPs) play in the drug discovery process, it remains extremely challenging to express, purify, and in vitro stabilize them for detailed biophysical analyses. Cell-free transcription-translation systems have emerged as a promising alternative for producing complex proteins, but they are still not a viable option for expressing IMPs due to improper post-translational folding of these proteins. We have studied key factors influencing in vitro folding of cell-free-expressed IMPs, particularly oligomeric proteins (i.e., ion channels). Using a chimeric ion channel, KcsA-Kv1.3 (K-K), as a model IMP, we have investigated several physiochemical determinants including artificial bilayer environments (i.e., lipid, detergent) for K-K in vitro stabilization. We observed that fusion of a ‘superfolder’ green fluorescent protein (sfGFP) to K-K as a protein expression reporter not only improves the protein yield, but surprisingly facilitates the K-K tetramer formation, probably by enhancing the solubility of monomeric K-K. Additionally, anionic lipids (i.e., DMPG) were found to be essential for the correct folding of cell-free-expressed monomeric K-K into tetramer, underscoring the importance of lipid-protein interaction in maintaining structural-functional integrity of ion channels. We further developed methods to integrate cell-free-expressed IMPs directly onto a biosensor chip. We employed a solid-supported lipid bilayer onto the surface plasmon resonance (SPR) chip to insert nascent K-K in a membrane. In a different approach, an anti-GFP-functionalized surface was used to capture in situ expressed K-K via its sfGFP tag. Interestingly, only the K-K-functionalized capture surface prepared by the latter strategy was able to interact with K-K's small binding partners. This generalizable approach can be further extended to other membrane proteins for developing direct binding assays involving small ligands.  +
In this chapter, we present a framework for online control customization that makes use of finite-horizon, optimal control combined with real-time trajectory generation and optimization. The results are based on a novel formulation of receding-horizon optimal control that replaces the traditional terminal constraints with a control Lyapunov function-based terminal cost. This formulation leads to reduced computational requirements and allows proof of stability under a variety of realistic assumptions on computation. By combining these theoretical advances with advances in computational power for real-time, embedded systems, we demonstrate the efficacy of online control customization via optimization-based control. The results are demonstrated using a nonlinear, flight control experiment at Caltech.  +
Temporal logics have proven effective for correct-by-construction synthesis of controllers for a wide range of applications. Receding horizon frameworks mitigate the computational intractability of reactive synthesis for temporal logic, but have thus far been limited by pursuing a single sequence of short horizon problems to the current goal. We propose a receding horizon algorithm for reactive synthesis that automatically determines a path to the currently pursued goal at runtime, in response to a nondeterministic environment. This is achieved by allowing each short horizon to have multiple local goals, and determining which local goal to pursue based on the current global goal, currently perceived environment and a pre-computed invariant dependent on each global goal. We demonstrate the utility of this additional flexibility in grant-response tasks, using a search-and-rescue example. Moreover, we show that these goal-dependent invariants mitigate the conservativeness of the receding horizon approach.  +
In this paper we investigate the optimal control of affine connection control systems. The formalism of the affine connection can be used to describe geometrically the dynamics of me chanical systems, including those with nonholonomic constraints. In the standard variational approach to such problems, one converts an n dimensional second order system into a 2n dimensional first order system, and uses these equations as constraints on the optimization. An alternative approach, which we develop in this paper, is to include the system dynamics as second order constraints of the optimization, and optimize relative to variations in the configuration space. Using the affine connection, its associated tensors, and the notion of covariant differentiation, we show how variations in the configuration space induce variations in the tangent space. In this setting, we derive second order equations have a geometric formulation parallel to that of the system dynamics. They also specialize to results found in the literature.  +
We develop a framework for optimal control policy synthesis for non-deterministic transition systems subject to temporal logic specifications. We use a fragment of temporal logic to specify tasks such as safe navigation, response to the environment, persistence, and surveillance. By restricting specifications to this fragment, we avoid a potentially doubly-exponential automaton construction. We compute feasible con- trol policies for non-deterministic transition systems in time polynomial in the size of the system and specification. We also compute optimal control policies for average, minimax (bottleneck), and average cost-per-task-cycle cost functions. We highlight several interesting cases when these can be computed in time polynomial in the size of the system and specification. Additionally, we make connections between computing optimal control policies for an average cost-per-task-cycle cost function and the generalized traveling salesman problem. We give simulation results for motion planning problems.  +
We present a mathematical programming-based method for optimal con- trol of nonlinear systems subject to temporal logic task specifications. We specify tasks using a fragment of linear temporal logic (LTL) that allows both finite- and infinite-horizon properties to be specified, including tasks such as surveillance, periodic motion, repeated assembly, and environmental monitoring. Our method di- rectly encodes an LTL formula as mixed-integer linear constraints on the system variables, avoiding the computationally expensive process of creating a finite ab- straction. Our approach is efficient; for common tasks our formulation uses significantly fewer binary variables than related approaches and gives the tightest possible convex relaxation. We apply our method on piecewise affine systems and certain classes of differentially flat systems. In numerical experiments, we solve temporal logic motion planning tasks for high-dimensional (10+) continuous systems.  +
We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks.  +
The fact that genes compete for shared cellular resources poses a fundamental challenge when identifying pa- rameters of synthetic gene circuits. A recently developed model of gene expression tackles this problem by explicitly accounting for resource competition. In addition to accurately describing experimental data, this model only depends on a handful of easily identifiable parameters with clear physical interpretation. Based on this model, we outline a procedure how to select the optimal set of experiments to characterize biomolecular parts in synthetic biology. Additionally, we reveal the role competition for shared resources plays, provide guidelines how to minimize its detrimental effects, and how to leverage this phenomenon to extract the most information about unknown parameters. To illustrate the results, we consider the case of part characterization in cell-free extracts, treat plasmid DNA concentrations as decision variables, and demonstrate the significant performance difference between na ̈ıve and optimal experiment design.  +
We examine optimal Linear Quadratic Gaussian control for a system in which communication between the sensor (output of the plant) and the controller occurs across a packet-dropping link. We extend the familiar LQG separation principle to this problem that allows us to solve this problem using a standard LQR state-feedback design, along with an optimal algorithm for propagating and using the information across the unreliable link. We present one such optimal algorithm, which consists of a Kalman Filter at the sensor side of the link, and a switched linear filter at the controller side. Our design does not assume any statistical model of the packet drop events, and is thus optimal for an arbitrary packet drop pattern. Further, the solution is appealing from a practical point of view because it can be implemented as a small modification of an existing LQG control design.  +
We examine two special cases of the problem of optimal linear quadratic Gaussian control of a system whose state is being measured by sensors that communicate with the controller over packet-dropping links. We pose the problem as an  +
In this paper we consider state estimation carried over a sensor network. A fusion center forms a local multi-hop tree of sensors and gateways and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. The number of hops that the sensors use to communicate data with the fusion center is optimized such that either the overall transmission energy is minimized or the network lifetime is maximized. In both cases the fusion center provides a specified level of estimation accuracy. Some heuristic algorithms are proposed which lead to suboptimal solutions in the energy minimization problem, while an algorithm that leads to the global optimal solution is proposed in the lifetime maximization problem. In both cases, the algorithms are shown to have low computational complexity. Examples are provided to demonstrateand algorithms.  +
Control of vehicle formations has emerged as a topic of significant interest to the controls community. In applications such as microsatellites and underwater vehicles, formations have the potential for greater functionality and versatility than individual vehicles. In this thesis, we investigate two topics relevant to control of vehicle formations: optimal vehicle control and cooperative control.  +
Development of feasible G&C (guidance and control) methods for precision atmospheric re-entry has remained a challenge since pre-Apollo-era space exploration. The inherent difficulty arises from the governing hypersonic dynamics being significantly nonlinear, subject to parametric uncertainty, and limited with control authority. Vehicle safety requirements impose further constraints, and desired cost objectives complicate an already difficult G&C problem. The scope of this paper is to present a guidance algorithm for optimal trajectory generation based on a reduced-dimension reentry formulation. Preliminary simulations demonstrate the algorithm with feedback used to track the guidance trajectory in the presence of initial state uncertainty. The objective is to further this approach toward an onboard receding-horizon implementation  +
This research addresses the path planning problem with a nonlinear optimization method running in real time. An optimization problem is continually solved to find a time-optimal, dynamically feasible trajectory from the vehicleâs position to some receding horizon ahead (20m-70m forward). The locally optimal numerical solver optimizes both the spatial and temporal components of the trajectory simultaneously, and feeds its output to a trajectory-following controller. The method has been implemented and tested on a modified Ford E350 van. Using one stereo pair and four LADAR units as terrain sensors, the vehicle was able to consistently traverse a 2 mile obstacle course at the DGC qualifying event. At the main DGC event, the vehicle drove 8 autonomous miles through the Nevada desert before experiencing non-planning issues. During this time, the planning system generated a plan 4.28 times per second on average. This execution speed, coupled with a feedback-based trajectory-following controller was shown to be adequate at providing smooth and reliable obstacle avoidance even on complicated terrain.  +