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Hard Limits And Performance Tradeoffs In A Class Of Sequestration Feedback Systems + (Feedback regulation is pervasive in biolog … Feedback regulation is pervasive in biology at both the organismal and cellular level. In this article, we explore the properties of a particular biomolecular feedback mechanism implemented using the sequestration binding of two molecules. Our work develops an analytic framework for understanding the hard limits, performance tradeoffs, and architectural properties of this simple model of biological feedback control. Using tools from control theory, we show that there are simple parametric relationships that determine both the stability and the performance of these systems in terms of speed, robustness, steady-state error, and leakiness. These findings yield a holistic understanding of the behavior of sequestration feedback and contribute to a more general theory of biological control systems.eral theory of biological control systems.)
Flat systems, equivalence and trajectory generation + (Flat systems, an important subclass of non … Flat systems, an important subclass of nonlinear control systems introducedvia differential-algebraic methods, are deﬁned in a differentialgeometric framework. We utilize the inﬁnite dimensional geometry developedby Vinogradov and coworkers: a control system is a diffiety, or moreprecisely, an ordinary diffiety, i.e. a smooth inﬁnite-dimensional manifoldequipped with a privileged vector ﬁeld. After recalling the deﬁnition ofa Lie-Backlund mapping, we say that two systems are equivalent if theyare related by a Lie-Backlund isomorphism. Flat systems are those systemswhich are equivalent to a controllable linear one. The interest ofsuch an abstract setting relies mainly on the fact that the above systemequivalence is interpreted in terms of endogenous dynamic feedback. Thepresentation is as elementary as possible and illustrated by the VTOLaircraft.rcraft.)
The Dynamics of Thin Film Growth: A Modeling Study + (For closed-loop control of thin film depos … For closed-loop control of thin film deposition, one would like todirectly control film properties such as roughness, stress, orcomposition, rather than process parameters liketemperatures and flow rates. This requires amodel of the dynamic response of film properties tochanges in process conditions. Direct atomistic simulation is far too slow to be used in thiscapacity, but a promising approach we explore here is to derivereduced-order dynamic models from atomistic simulations.In this paper, we consider film growth on a vicinal surfaceusing a kinetic MonteCarlo model. The temperature range spans the transition fromsmooth step flow to rough island growth.Proper Orthogonal Decomposition is used to extractthe dominant spatial modes from the KMC simulations. Only five spatial modesadequately represent the roughness dynamics for all simulated times andtemperatures, indicating that a 5-state model may besufficient for real-time roughness control.y be sufficient for real-time roughness control.)
State Estimation Utilization Multiple Description Coding over Lossy Networks + (For state estimation in networked control … For state estimation in networked control systems,the impact of packet dropping and delay over network links isan important problem. In this paper, we introduce multiple description(MD) source coding scheme to improve the statisticalstability and performance of the estimation error covarianceof Kalman filtering with packet loss. We consider about twocases: when the packet loss over network links occurs in an i.i.d.fashion or in a bursty fashion. Compared with the traditionalsingle description source coding, MD coding scheme can greatlyimprove the performance of Kalman filtering over a large setof packet loss scenarios in both cases.et of packet loss scenarios in both cases.)
State Estimation Over Packet Dropping Networks Using Multiple Description Coding + (For state estimation over a communication … For state estimation over a communication network, efficiency and reliability of the network are critical issues. The presence of packet dropping and communication delay can greatly impair our ability to measure and predict states. In this paper, multiple description (MD) codes, a type of network source codes, are used to compensate for this effect on Kalman filtering. We consider two packet dropping models: in one model, packet dropping occurs according to an independent and identically distributed (i.i.d.) Bernoulli random process and in the other model, packet dropping is bursty and occurs according to a Markov chain. We show that MD codes greatly improve the statistical stability and performance of Kalman filter over a large set of packet loss scenarios in both cases. Our conclusions are verified by simulation results.usions are verified by simulation results.)
Parallelizing Synthesis from Temporal Logic Specifications by Identifying Equicontrollable States + (For the synthesis of correct-by-constructi … For the synthesis of correct-by-construction control policies from temporal logic specifications the scalability of the synthesis algorithms is often a bottleneck. In this paper, we parallelize synthesis from specifications in the GR(1) fragment of linear temporal logic by introducing a hierarchical procedure that allows decoupling of the fixpoint computations. The state space is partitioned into equicontrollable sets using solutions to parameterized reachability games that arise from decomposing the original GR(1) game into smaller reachability games. Following the partitioning, another synthesis problem is formulated for composing the strategies from the decomposed reachability games. The formulation guarantees that composing the synthesized controllers ensures satisfaction of the given GR(1) property. Benchmarking experiments with robot planning problems demonstrate good scalability of the approach.onstrate good scalability of the approach.)
Analysis of a Digital Clock for Molecular Computing + (Gene expression is often controlled by nat … 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.ceptual foundations of these improvements.)
Regulatory activity revealed by dynamic correlations in gene expression noise + (Gene regulatory interactions are context d … Gene regulatory interactions are context dependent, active in some cellular states but not in others. Stochastic fluctuations, or 'noise', in gene expression propagate through active, but not inactive, regulatory links. Thus, correlations in gene expression noise could provide a noninvasive means to probe the activity states of regulatory links. However, global, 'extrinsic', noise sources generate correlations even without direct regulatory links. Here we show that single-cell time-lapse microscopy, by revealing time lags due to regulation, can discriminate between active regulatory connections and extrinsic noise. We demonstrate this principle mathematically, using stochastic modeling, and experimentally, using simple synthetic gene circuits. We then use this approach to analyze dynamic noise correlations in the galactose metabolism genes of Escherichia coli. We find that the CRP-GalS-GalE feed-forward loop is inactive in standard conditions but can become active in a GalR mutant. These results show how noise can help analyze the context dependence of regulatory interactions in endogenous gene circuits. interactions in endogenous gene circuits.)
Delay-dependent Stability of Genetic Regulatory Networks + (Genetic regulatory networks are biochemica … Genetic regulatory networks are biochemical reaction systems, consisting of a network of interacting genes and associated proteins. The dynamics of genetic regulatory networks contain many complex facets that require careful consideration during the modeling process. The classical modeling approach involves studying systems of ordinary differential equations (ODEs) that model biochemical reactions in a deterministic, continuous, and instantaneous fashion. In reality, the dynamics of these systems are stochastic, discrete, and widely delayed. The first two complications are often successfully addressed by modeling regulatory networks using the Gillespie stochastic simulation algorithm (SSA), while the delayed behavior of biochemical events such as transcription and translation are often ignored due to their mathematically difficult nature. We develop techniques based on delay-differential equations (DDEs) and the delayed Gillespie SSA to study the effects of delays, in both continuous deterministic and discrete stochastic settings. Our analysis applies techniques from Floquet theory and advanced numerical analysis within the context of delay-differential equations, and we are able to derive stability sensitivities for biochemical switches and oscillators across the constituent pathways, showing which pathways in the regulatory networks improve or worsen the stability of the system attractors. These delay sensitivities can be far from trivial, and we offer a computational framework validated across multiple levels of modeling fidelity. This work suggests that delays may play an important and previously overlooked role in providing robust dynamical behavior for certain genetic regulatory networks, and perhaps more importantly, may offer an accessible tuning parameter for robust bioengineering.uning parameter for robust bioengineering.)
Differential Flatness of Two One-Forms in Arbitrary Number of Variables + (Given a differentially flat system of ODEs … Given a differentially flat system of ODEs, flat outputs that depend only on originalvariables but not on their derivatives are called zero-flat outputs and systems possessingsuch outputs are called zero-flat. In this paper we present a theory of zero-flatness fora system of two one-forms in arbitrary number of variables $(t,x^1,\dots,x^N)$. Ourapproach splits the task of finding zero-flat outputs into two parts. First part involvessolving for distributions that satisfy a set of algebraic conditions. If the first parthas no solution then the system is not zero-flat. The second part involves finding anintegrable distribution from the solution set of the first part. Typically this partinvolves solving PDEs. Our results are also applicable in determining if a control affinesystem in $n$ states and $n-2$ controls has flat outputs that depend only on states. Weillustrate our method by examples.tes. We illustrate our method by examples.)
Grasping with Flexible Link Fingers: An Initial Study + (Grasping with flexible fingers presents an … Grasping with flexible fingers presents an attractive approach forcertain robotic tasks. Its implementation requires simultaneousposition and force control of flexible manipulators, an area aboutwhich there is little information in the literature. This paperpresents an initial effort at designing controllers for flexible linkrobots to control both position and force. The analysis is done on atwo degree-of-freedom two-link manipulator with the last linkflexible. A control strategy is proposed and asymptotic stability isproved. Results from using this control law in simulations and on anexperimental setup are presented.nd on an experimental setup are presented.)
Convex optimal uncertainty quantification: Algorithms and a case study in energy storage placement for power grids + (How does one evaluate the performance of a … How does one evaluate the performance of a stochastic system in the absence of a perfect model (i.e. probability distribution)? We address this question under the framework of optimal uncertainty quantification (OUQ), which is an information-based approach for worst-case analysis of stochastic systems. We are able to generalize previous results and show that the OUQ problem can be solved using convex optimization when the function under evaluation can be expressed in a polytopic canonical form (PCF). We also propose iterative methods for scaling the convex formulation to larger systems. As an application, we study the problem of storage placement in power grids with renewable generation. Numerical simulation results for simple artificial examples as well as an example using the IEEE 14-bus test case with real wind generation data are presented to demonstrate the usage of OUQ analysis. to demonstrate the usage of OUQ analysis.)
Protocols for Implementing an Escherichia coli Based TX-TL Cell-Free Expression System for Synthetic Biology + (Ideal cell-free expression systems can the … Ideal cell-free expression systems can theoretically emulate an in vivo cellular environment in a controlled in vitro platform. This is useful for expressing proteins and genetic circuits in a controlled manner as well as for providing a prototyping environment for synthetic biology. To achieve the latter goal, cell-free expression systems that preserve endogenous Escherichia coli transcription-translation mechanisms are able to more accurately reflect in vivo cellular dynamics than those based on T7 RNA polymerase transcription. We describe the preparation and execution of an efficient endogenous E. coli based transcription-translation (TX-TL) cell-free expression system that can produce equivalent amounts of protein as T7-based systems at a 98% cost reduction to similar commercial systems. The preparation of buffers and crude cell extract are described, as well as the execution of a three tube TX-TL reaction. The entire protocol takes five days to prepare and yields enough material for up to 3000 single reactions in one preparation. Once prepared, each reaction takes under 8 hr from setup to data collection and analysis. Mechanisms of regulation and transcription exogenous to E. coli, such as lac/tet repressors and T7 RNA polymerase, can be supplemented.6 Endogenous properties, such as mRNA and DNA degradation rates, can also be adjusted.7 The TX-TL cell-free expression system has been demonstrated for large-scale circuit assembly, exploring biological phenomena, and expression of proteins under both T7- and endogenous promoters. Accompanying mathematical models are available. The resulting system has unique applications in synthetic biology as a prototyping environment, or "TX-TL biomolecular breadboard."nment, or "TX-TL biomolecular breadboard.")
Robust Safe Control Synthesis with Disturbance Observer-Based Control Barrier Functions + (In a complex real-time operating environme … In a complex real-time operating environment, external disturbances and uncertainties adversely affect the safety, stability, and performance of dynamical systems. This paper presents a robust stabilizing safety-critical controller synthesis framework with control Lyapunov functions (CLFs) and control barrier functions (CBFs) in the presence of disturbance. A high-gain input observer method is adapted to estimate the time-varying unmodelled dynamics of the CBF with an error bound using the first-order time derivative of the CBF. This approach leads to an easily tunable low order disturbance estimator structure with a design parameter as it utilizes only the CBF constraint. The estimated unknown input and associated error bound are used to ensure robust safety and exponential stability by formulating a CLF-CBF quadratic program. The proposed method is applicable to both relative degree one and higher relative degree CBF constraints. The efficacy of the proposed approach is demonstrated using a numerical simulations of an adaptive cruise control system and a Segway platform with an external disturbance.way platform with an external disturbance.)
A Contract-Based Methodology for Aircraft Electric Power System Design + (In an aircraft electric power system, one … 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.f-of-concept electric power system design.)
Leveraging Classification Metrics for Quantitative System-Level Analysis with Temporal Logic Specifications + (In many autonomy applications, performance … In many autonomy applications, performance of perception algorithms is important for effective planning and control. In this paper, we introduce a framework for computing the probability of satisfaction of formal system specifications given a confusion matrix, a statistical average performance measure for multi-class classification. We define the probability of satisfaction of a linear temporal logic formula given a specific initial state of the agent and true state of the environment. Then, we present an algorithm to construct a Markov chain that represents the system behavior under the composition of the perception and control components such that the probability of the temporal logic formula computed over the Markov chain is consistent with the probability that the temporal logic formula is satisfied by our system. We illustrate this approach on a simple example of a car with pedestrian on the sidewalk environment, and compute the probability of satisfaction of safety requirements for varying parameters of the vehicle. We also illustrate how satisfaction probability changes with varied precision and recall derived from the confusion matrix. Based on our results, we identify several opportunities for future work in developing quantitative system-level analysis that incorporates perception models.lysis that incorporates perception models.)
Effect of Narrowband Channels on the Control + (In mobile sensor networks, sensor measurem … In mobile sensor networks, sensor measurementsas well as control commands are transmitted overwireless time-varying links. It then becomes considerablyimportant to address the impact of imperfect communicationon the overall performance. In this paper, westudy the effect of time-varying communication links onthe control performance of a mobile sensor node. Inparticular, we investigate the impact of fading. We derivekey performance measure parameters to evaluate theoverall feedback control performance over narrowbandchannels. We show that fading can result in considerabledelay and/or poor performance of the mobile sensordepending on the system requirements. To improve theperformance, we then show how the application layer canuse the channel status information of the physical layerto adapt control commands accordingly. We show thatsharing information across layers can improve the overallperformance considerably. We verify our analyticalresults by simulating a wireless speed control problem.mulating a wireless speed control problem.)
Synthetic mammalian signaling circuits for robust cell population control + (In multicellular organisms, cells actively … In multicellular organisms, cells actively sense, respond to, and control their own population density. Synthetic mammalian quorum sensing circuits could provide insight into principles of population control and improve cell therapies. However, a key challenge is avoiding their inherent sensitivity to “cheater” mutations that evade control. Here, we repurposed the plant hormone auxin to enable orthogonal mammalian cell-cell communication and quorum sensing. Further, we show that a “paradoxical” circuit design, in which auxin stimulates and inhibits net cell growth at different concentrations, achieves population control that is robust to cheater mutations, controlling growth for 43 days of continuous culture. By contrast, a non-paradoxical control circuit limited growth but was susceptible to mutations. These results establish a foundation for future cell therapies that can respond to and control their own population sizes.to and control their own population sizes.)
When are Distributed Algorithms Robust? + (In recent years, numerous distributed algo … In recent years, numerous distributed algorithms have been proposed which, when executed by a team of dynamic agents, result in the completion of a joint task. However, for any such algorithm to be practical, one should be able to guarantee that the task is still satisfactorily executed even when agents fail to communicate with others or to perform their designated actions correctly. In this paper, we present a concept of robustness which is well-suited for general distributed algorithms for teams of dynamic agents. Our definition extends a similar notion introduced in the distributed computation literature for consensus problems. We illustrate the definition by considering a variety of algorithms.on by considering a variety of algorithms.)
Towards Formal Synthesis of Reactive Controllers for Dexterous Robotic Manipulation + (In robotic finger gaiting, fingers continu … In robotic finger gaiting, fingers continuously manipulate an object until joint limitations or mechanical limitations periodically force a switch of grasp. Current approaches to gait planning and control are slow, lack formal guarantees on correctness, and are generally not reactive to changes in object geometry. To address these issues, we apply advances in formal methods to model a gait subject to external perturbations as a two-player game between a finger controller and its adversarial environment. High-level specifications are expressed in linear temporal logic (LTL) and low-level control primitives are designed for continuous kinematics. Simulations of planar manipulation with our synthesized correct-by-construction gait controller demonstrate the benefits of this approach.demonstrate the benefits of this approach.)
Fast and flexible simulation and parameter estimation for synthetic biology using bioscrape + (In systems and synthetic biology, it is co … In systems and synthetic biology, it is common to build chemical reaction network (CRN) models of biochemical circuits and networks. Although automation and other high-throughput techniques have led to an abundance of data enabling data-driven quantitative modeling and parameter estimation, the intense amount of simulation needed for these methods still frequently results in a computational bottleneck. Here we present bioscrape (Bio-circuit Stochastic Single-cell Reaction Analysis and Parameter Estimation) - a Python package for fast and flexible modeling and simulation of highly customizable chemical reaction networks. Specifically, bioscrape supports deterministic and stochastic simulations, which can incorporate delay, cell growth, and cell division. All functionalities - reaction models, simulation algorithms, cell growth models, partitioning models, and Bayesian inference - are implemented as interfaces in an easily extensible and modular object-oriented framework. Models can be constructed via Systems Biology Markup Language (SBML) or specified programmatically via a Python API. Simulation run times obtained with the package are comparable to those obtained using C code - this is particularly advantageous for computationally expensive applications such as Bayesian inference or simulation of cell lineages. We show the package’s simulation capabilities on a variety of example simulations of stochastic gene expression. We also demonstrate the package by using it to do parameter inference on a model of integrase enzyme-mediated DNA recombination dynamics with experimental data. The bioscrape package is publicly available online (Pandey, Poole, et al., 2023) along with more detailed documentation and examples. more detailed documentation and examples.)
A Homotopy Algorithm for Approximating Geometric Distributions by Integrable Systems + (In the geometric theory of nonlinear contr … In the geometric theory of nonlinear control systems, the notion of a distribution andthe dual notion of codistribution play a central role. Many results in nonlinear controltheory require certain distributions to be integrable. Distributions (and codistributions)are not generically integrable and, moreover, the integrability property is not likely topersist under small perturbations of the system. Therefore, it is natural to consider theproblem of approximating a given codistribution by an integrable codistribution, and todetermine to what extent such an approximation may be used for obtaining approximatesolutions to various problems in control theory. In this note, we concentrate on thepurely mathematical problem of approximating a given codistribution by an integrablecodistribution. We present an algorithm for approximating an m-dimensional nonintegrablecodistribution by an integrable one using a homotopy approach. The method yields anapproximating codistribution that agrees with the original codistribution on anm-dimensional submanifold E_0 of R^n.n an m-dimensional submanifold E_0 of R^n.)
Uncertain semantics, representation nuisances, and necessary invariance properties of bootstrapping agents + (In the problem of bootstrapping, an agent … In the problem of bootstrapping, an agent must learn to use an unknown body, in an unknown world, starting from zero information about the world, its sensors, and its actuators. So far, this fascinating problem has not been given a proper formalization. In this paepr, we provide a possible rigorous definition of one of the key aspects of bootstrapping, namely the fact that an agent must be able to use âuninterpretedâ observations and commands. We show that this can be formalized by positing the existence of representation nuisances that act on the data, and which must be tolerated by an agent. The classes of nuisances tolerated indirectly encode the assumptions needed about the world, and therefore the agent's ability to solve smaller or larger classes of bootstrapping instances. Moreover, we argue that the behavior of an agent that claims optimality must actually be invariant to the representation nuisances, and we discuss several design principles to obtain such invariance.sign principles to obtain such invariance.)
Cone invariance and rendezvous of multiple agents + (In this article is presented a dynamical s … 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.emonstrate application are also presented.)
Online Control Customization via Optimization-Based Control + (In this chapter, we present a framework fo … In this chapter, we present a framework for online control customization thatmakes use of finite-horizon, optimal control combined with real-timetrajectory generation and optimization. The results are based on a novelformulation of receding-horizon optimal control that replaces the traditionalterminal constraints with a control Lyapunov function-based terminal cost.This formulation leads to reduced computational requirements and allows proofof stability under a variety of realistic assumptions on computation. Bycombining these theoretical advances with advances in computational power forreal-time, embedded systems, we demonstrate the efficacy of online controlcustomization via optimization-based control. The results are demonstratedusing a nonlinear, flight control experiment at Caltech.ear, flight control experiment at Caltech.)

(In this chapter, we present a framework for online control customization)

Decompositions for Control Systems on Manifolds with an Affine Connection + (In this letter we present a decomposition … In this letter we present a decomposition for control systems whose drift vector fieldis the geodesic spray associated with an affine connection. With the geometric insightgained with this decomposition, we are able to easily prove some special results for thisclass of control systems. Examples illustrate the theory.l systems. Examples illustrate the theory.)
On a Stochastic Sensor Selection Algorithm with Applications in Sensor Scheduling and Sensor Coverage + (In this note we consider the following pro … In this note we consider the following problem. Suppose a set of sensors is jointly trying to estimate a process. One sensor takes a measurement at every time step and the measurements are then exchanged among all the sensors. What is the sensor schedule that results in the mininmum error covariance? We describe a stoachastic sensor selection strategy that is easy to implement and is computationally tractable. The problem described above comes up in many domains out of which we discuss two. In the sensor selection problem, there are multiple sensors that cannot operate simultaneously (eg, sonars in the same frequency band). Thus measurements need to be scheduled. In the sensor coverage problem, a geographical area needs to be covered by mobile sensors each with limited range. Thus from every position, the sensors obtain a different viewpoint of the area and the sensors need to optimize their positions. The algorithm is applied to these problems and illustrated through simple examples.s and illustrated through simple examples.)
A Frequency Domain Condition for Stability of Interconnected MIMO Systems + (In this paper analysis of interconnected d … In this paper analysis of interconnected dynamical systemsis considered. A framework for the analysis of the stabilityof interconnection is given. The results from Fax andMurray that studies the SISO-case for a constant interconnectionmatrix are genralized to the MIMO-case wherearbitrary interconnection is allowed. The analysis show existnessof a separation principle that is very useful in thesense of the simplicity for stability analysis. Stability couldbe checked graphically using a Nyquist-like criterion. Theproblem with time-delays and interconnection variation androbustness appear to be natural special cases of the generalframework, and hence, simple stability criteria are derivedeasly.mple stability criteria are derived easly.)
Experimental Comparison of Trajectory Trackers for a Car with Trailers + (In this paper various design techniques ar … In this paper various design techniques are applied to the trajectory tracking problem for a mobilerobot with trailers. Using simulations and experiments, we evaluate linear and nonlinear designson the basis of implementation issues, stability and performance. After a careful design of theirgains, the various feedback controllers have very close performance measures. In both thesimulations and the experiments, all the controllers show a strong dependence on the knowledgeof the reference trajectory. The flatness of the system is exploited in precomputing this quantity.s exploited in precomputing this quantity.)
Effects of Noise, Magnitude Saturation, and Rate Limits on Rotating Stall Control + (In this paper we analyze the effects of fl … In this paper we analyze the effects of fluid noise, actuator bandwidth,magnitude saturation and rate limits on rotating stall control bystudying a two dimensional system which is the approximationof the dynamics on the attracting saddle-sink connections of the threestate low $B$ parameter Moore Greitzer model together with thedynamics of the bleed valve controller. We show that the region ofattraction to the stabilized rotating stall equilibria is seriously restrained by the fluid noise level, theactuator bandwidth, magnitude saturation and rate limits. Thebandwidth and rate requirement for a fixed extension of stable regionis estimated by calculating the stable manifold of the saddle fixedpoint of the two dimensional system.fixed point of the two dimensional system.)
Experiments in Exponential Stabilization of a Mobile Robot Towing a Trailer + (In this paper we apply some recently devel … In this paper we apply some recently developed control laws forstabilization of mechanical systems with nonholonomic constraints toan experimental system consisting of a mobile robot towing a trailer.We verify the applicability of various control laws which haveappeared in the recent literature, and compare the performance ofthese controllers in an experimental setting. In particular, we showthat time-periodic, non-smooth controllers can be used to achieveexponential stability of a desired equilibrium configuration, and thatthese controllers outperform smooth, time-varying control laws. Wealso point out several practical considerations which must be takeninto account when implementing these controllers.count when implementing these controllers.)
A hovercraft robot that uses insect-inspired visual autocorrelation for motion control in a corridor + (In this paper we are concerned with the ch … 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.nertial dynamics using purely correlators.)
Communication and Sensing Trade-Offs in Decentralized Mobile Sensor Networks: A Cross-Layer Design Approach + (In this paper we characterize the impact o … In this paper we characterize the impact of imperfect communicationon the performance of a decentralized mobile sensor network.We first examine and demonstrate the trade-offs between communicationand sensing objectives, by determining the optimal sensor configurationswhen introducing imperfect communication. We further illustrate theperformance degradation caused by non-ideal communication links ina decentralized mobile sensor network. To address this, we propose adecentralized motion-planning algorithm that considers communicationeffects. The algorithm is a cross-layer design based on the proper interfaceof physical and application layers. Simulation results will show theperformance improvement attained by utilizing this algorithm.ment attained by utilizing this algorithm.)
Estimation Over Wireless Sensor Networks: Tradeoff between Communication, Computation and Estimation Qualities + (In this paper we consider a state estimati … In this paper we consider a state estimation problem over a wireless sensor network. A fusion center dynamically forms a local multi-hop tree of sensors and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. Using estimation quality as a metric, two communication schemes are studied and compared. In scheme one, sensor nodes communicate measurement data to their parent nodes, while in scheme two, sensor nodes communicate their local state estimates to their parent nodes. We show that under perfect communication links, the two schemes produce the same estimate at the fusion center with unlimited computation at each sensor node; scheme one is always better than scheme two with limited computation. When data packet drops occur on the communication links, we show that scheme two always outperforms scheme one with unlimited computation; with limited computation, we show that there exists a critical packet arrival rate, above which, scheme one outperforms scheme two. Simulations are provided to demonstrate the two schemes under various circumstances.e two schemes under various circumstances.)
Feedback Stabilization of Steady-State and Hopf Bifurcations + (In this paper we consider nonlinear system … In this paper we consider nonlinear systems with steady-state or Hopf bifurcations forwhich the bifurcated modes are linearly uncontrollable. The goal is to find statefeedbacks such that the bifurcation for the closed loop system is supercritical, and atthe same time, the linearly controllable subsystem is asymptotically stable. Necessary andsufficient conditions for the non-existence of sufficiently smooth state feedbacks havebeen obtained under certain nondegeneracy conditions. For the cases when those conditionsare not satisfied, we give explicit constructions of the feedbacks. The construction hasthe following separation property: for any linear state feedback such that thecontrollable subsystem is asymptotically stable, we could construct gains in the nonlinearstate feedbacks such that the closed loop system is asymptotically stable at thebifurcation point.totically stable at the bifurcation point.)
Optimal Sensor Hop Selection: Sensor Energy Minimization and Network Lifetime Maximization with Guaranteed System Performance + (In this paper we consider state estimation … In this paper we consider state estimation carried over a sensor network. A fusion center forms a local multi-hop tree of sensors and gateways and fuses the data into a state estimate. It is shown that the optimal estimator over a sensor tree is given by a Kalman filter of certain structure. The number of hops that the sensors use to communicate data with the fusion center is optimized such that either the overall transmission energy is minimized or the network lifetime is maximized. In both cases the fusion center provides a specified level of estimation accuracy. Some heuristic algorithms are proposed which lead to suboptimal solutions in the energy minimization problem, while an algorithm that leads to the global optimal solution is proposed in the lifetime maximization problem. In both cases, the algorithms are shown to have low computational complexity. Examples are provided to demonstrateand algorithms.are provided to demonstrateand algorithms.)
Optimum Allocation of Computing Resources in Networked Sensing and Control + (In this paper we consider task scheduling … In this paper we consider task scheduling whensensing and controlling over a network with packet droppinglinks. We find optimum ways of allocating limited computingresources for estimation and control of a numberof linear dynamical systems with different characteristicsover communication links with different qualities. We findtheoretical expressions relating the optimum sampling rates tothe characteristics of the communication links and dynamics ofthe plants.When considering resource allocation for estimationof the plants, we derive optimum ways of task scheduling fortwo performance metrics: decay rate and the asymptotic valueof the estimation error variance. When scheduling the controltasks, we consider rate of convergence of the state and theoverall control cost as performance measures. The work laysthe theoretical foundations for considering the impact of bothlimited computing and communication resources on estimationand control.ation resources on estimation and control.)
Communication and sensing trade-offs in cooperative mobile networks + (In this paper we consider the impact of co … 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. and extend a number of key results to 2D.)
Trajectory Generation for a Towed Cable System using Differential Flatness + (In this paper we consider the problem of g … In this paper we consider the problem of generating feasible motionsfor a towed cable, flight control system that has been proposed foruse in remote sensor applications. Using the fact that the system isdifferentially flat, we illustrate how to construct feasibletrajectories for the system and demonstrate the strengths andlimitations of this approach. Simulations of the full dynamics areincluded to illustrate the proposed techniques. A significantlimitation of the current approach is the numerical instability of thealgorithm, resulting in the need for careful tuning of parameters toachieve convergence.ning of parameters to achieve convergence.)
Observers for a Class of Hybrid Systems on a Lattice + (In this paper we consider the problem of e … In this paper we consider the problem of estimating discretevariables in a class of hybrid systems where we assume that the continuousvariables are available for measurement. Using lattice and ordertheory we develop a framework for constructing an observer on an enlargedspace of variables with lattice structure, which updates only twovariables at each step. We apply our ideas to a multi-robot system example,the RoboFlag Drill.-robot system example, the RoboFlag Drill.)
Global Dynamical Structure Reconstruction from Reconstructed Dynamical Structure Subnetworks: Applications to Biochemical Reaction Networks + (In this paper we consider the problem of n … In this paper we consider the problem of network reconstruction, with applications to biochemical reaction networks. In particular, we consider the problem of global network reconstruction when there are a limited number of sensors that can be used to simultaneously measure state information. We introduce dynamical structure functions as a way to formulate the network reconstruction problem and motivate their usage with an example physical system from synthetic biology. In particular, we argue that in synthetic biology research, network verification is paramount to robust circuit operation and thus, network reconstruction is an invaluable tool. Nonetheless, we argue that existing approaches for reconstruction are hampered by limited numbers of biological sensors with high temporal resolution. In this way, we motivate the global network reconstruction problem using partial network information and prove that by performing a series of reconstruction experiments, where each experiment reconstructs a subnetwork dynamical structure function, the global dynamical structure function can be recovered in most cases. We illustrate these reconstruction techniques on a recently developed four gene biocircuit, an event detector, and show that it is capable of differentiating the temporal order of input events.iating the temporal order of input events.)
Modeling Environmental Disturbances with the Chemical Master Equation + (In this paper we consider the problem of r … In this paper we consider the problem of repre- senting a biological system and its environment using a stochas- tic modeling framework. We first introduce a decomposition of the global chemical reaction system into two systems: a system of interest and its environment. We then present and derive a decomposition of the chemical master equation to achieve a representation describing the dynamics of the system of inter- est, perturbed by an environmental disturbance. We use this decomposition to model examples of two types of environmental disturbances: the disturbance a system experiences through loading effects from limited resources and the disturbance a system experiences when perturbed by an antibiotic that modifies transcription or translation rates.difies transcription or translation rates.)
Kinetic Monte Carlo Simulation of Dynamic Phenomena in Thin Film Growth + (In this paper we describe the response of … In this paper we describe the response of a Kinetic Monte Carlo model to time-varying growth conditions. We vary temperature and partial pressure sinusoidally and identify behavior typical of low-dimensional nonlinear systems. In particular, the frequency content of the roughness response is sensitive to the presence of steps in the surface.e to the presence of steps in the surface.)
A Risk-Aware Architecture for Resilient Spacecraft Operations + (In this paper we discuss a resilient, risk … 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.e RSE for a simulated Mars rover scenario.)
Application of Correct-by-Construction Principles for a Resilient Risk-Aware Architecture + (In this paper we discuss the application o … 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.ess to a simple rover resilience scenario.)
Evaluation of Bleed Valve Rate Requirements in Nonlinear Control of Rotating Stall + (In this paper we evaluate the actuator rat … In this paper we evaluate the actuator rate requirements for control of rotating stallusing a bleed valve and provide tools for predicting these requirements. Modification ofboth the stable and unstable parts of the compressor characteristic via addition ofcontinuous air injection serves to reduce the requirement of a bleed valve used for thepurpose of rotating stall stabilization. Analytical tools based on low order models (2-3states) and simulation tools based on a reduced order model (37 states) are described. Ableed actuator rate limit study is presented to compare the actuator requirementspredicted by theory, simulation, and experiment. The comparisons show that the predictionsobtained from theory and simulations share the same trend as the experiments, withincreasing accuracy as the complexity of the underlying model increases. Some insights onthe design of a bleed-compressor pair are given.sign of a bleed-compressor pair are given.)
Delay-Based Approximations of Biological Systems for Analysis and Design + (In this paper we explore the use of time-d … In this paper we explore the use of time-delayed differential equation as a means of obtaining a simplified description of very high order dynamics.This paper finds results for a particular type of system, a single-input single-output (SISO) linear system with a nonlinear feedback. We begin with a high dimensional system in state space and reduce the dimension by finding a delay based approximation which could be a smaller set of integro-differential equations or DDEs. We argue that approximations of high order linear subsystems whose distribution functions have relatively smaller variance such as delta functions, give a conservative approximation of a system's stable parameter space. Through examples inspired by biology, we show how these approximations can be used to verify stability. We analyze the system's stability and robustness dependence on statistical properties, mainly relative variance and expectation for a symmetric distribution function.ion for a symmetric distribution function.)
Differential Flatness and Absolute Equivalence of Nonlinear Control Systems + (In this paper we give a formulation of dif … In this paper we give a formulation of differential flatness---a concept originallyintroduced by Fleiss, Levine, Martin, and Rouchon---in terms of absolute equivalencebetween exterior differential systems. Systems which are differentially flat have severaluseful properties which can be exploited to generate effective control strategies fornonlinear systems. The original definition of flatness was given in the context ofdifferentiable algebra, and required that all mappings be meromorphic functions. Ourformulation of flatness does not require any algebraic structure and allows one to usetools from exterior differential systems to help characterize differentially flat systems.In particular, we shown that in the case of single input control systems (i.e.,codimension 2 Pfaffian systems), a system is differentially flat if and only if it isfeedback linearizable via static state feedback. However, in higher codimensions feedbacklinearizability and flatness are *not* equivalent: one must be careful with the role oftime as well the use of prolongations which may not be realizable as dynamic feedbacks ina control setting. Applications of differential flatness to nonlinear control systems andopen questions will be discussed.tems and open questions will be discussed.)
The Caltech Multi-Vehicle Wireless Testbed + (In this paper we introduce the Caltech Mul … In this paper we introduce the CaltechMulti-Vehicle Wireless Testbed (MVWT), a platform for testingdecentralized control methodologies for multiple vehiclecoordination and formation stabilization. The testbed consists ofeight mobile vehicles, an overhead vision system providingGPS-like position information and wireless Ethernet forcommunications. Each vehicle rests on omni-direction casters andis powered by two high-performance ducted fans. Thus, a uniquefeature of our testbed is that the vehicles have second orderdynamics, requiring real-time feedback algorithms to stabilize thesystem while performing cooperative tasks. The testbed will beused by various research groups at Caltech and elsewhere as ameans to validate theoretical advances in multiple-vehiclecoordination and control, networked control systems, real timenetworking and high confidence distributed computation.d high confidence distributed computation.)
Nonholonomic Motion Planning: Steering Using Sinusoids + (In this paper we investigate methods for s … In this paper we investigate methods for steering systems with nonholonomicconstraints between arbitrary configurations. Early work by Brockett derives the optimalcontrols for a set of canonical systems in which the tangent space to the configurationmanifold is spanned by the input vector fields and their first order Lie brackets. UsingBrockett's result as motivation, we derive suboptimal trajectories for systems which arenot in canonical form and consider systems in which it takes more than one level ofbracketing to achieve controllability. These trajectories use sinusoids at integrallyrelated frequencies to achieve motion at a given bracketing level. We define a class ofsystems which can be steered using sinusoids (chained systems) and give conditions underwhich a class of two-input systems can be converted into this form.t systems can be converted into this form.)

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