# 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.  +
Due to the increasing complexity of space missions and distance to exploration targets, future robotic systems used for space exploration call for more resilience and autonomy. Instead of minimizing the failure risk, we are focusing on missions that will inevitably encounter significant failures and are developing an algorithm that will autonomously reconfigure the system controller to continue to make progress towards the mission goal despite being in a reduced capacity state - we call this extreme resilience. In this paper, we develop a model-free framework to autonomously react to locomotion failures of robotic systems. This is done by the use of a neural network for path planning using the neuroevolution of aug- menting topologies (NEAT) algorithm and a dynamic database of possible moves and their effect on the system’s position and orientation. Two modes of failure detection and resolution are being introduced: (a) relative position failure detection, which is triggered by large, unexpected moves and results in a complete update of the database before a retraining of the neural network, and (b) absolute position failure detection, which triggers from large build-ups of position error from small failures and will induce a retraining of the neural network without an explicit database reset. We implement and validate this framework on a high-fidelity planetary rover simulation using Unreal Engine and on a hardware setup of a TurtleBot2 with a PhantomX Pincher robot arm.  +
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.  +