# Property:Abstract

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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.  +