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• This paper presents the use of pulsed air … This paper presents the use of pulsed air injection to control the onset of rotating</br>stall in a low-speed, axial flow compressor. By measuring the unsteady pressures near the</br>rotor face, a control algorithm determines the magnitude and phase of the first mode of</br>rotating stall and controls the injection of air in the front of the rotor face.</br>Experimental results show that this technique slightly extends the stall point of the</br>compressor and eliminates the hysteresis loop normally associated with rotating stall. A</br>parametric study is used to determine the optimal control parameters for suppression of</br>stall. Analytic results---using a low-dimensional model developed by Moore and Greitzer</br>combined with an unsteady shift in the compressor characteristic to model the</br>injectors---give further insights into the operation of the controller. Based on this</br>model, we show that the behavior of the experiment can be explained as a change in the</br>bifurcation behavior of the system under nonlinear feedback. A higher fidelity simulation</br>model is then used to further verify some of the specific performance characteristics that</br>are observed in experiments.eristics that are observed in experiments.  +
• This paper proposes a method of improving … This paper proposes a method of improving per- formance of scalar discrete-time systems with substantial delay by adding additional delayed feedback channels (i.e. imposing a distributed delay feedback). The optimal weights for the added feedback channels are found using optimization techniques. In particular, we reduce the H1 norm of the closed loop transfer function with multiple delayed feedback using techniques from static output feedback design. We impose constraints on the feedback gain in order to highlight the effectiveness of the distribution. In this manner, improvement on performance is a result of the distribution and not a change in the overall effective gain. The concept of applying a multiple delayed feedback channel is inspired by biological systems, where substantial delays can be present in feedback control. To show the effectiveness of this idea we apply our method to an example of a scalar genetic autoregulatory network. The constraint on the gain allows one to implement the feedback in a genetic regulatory network without having to change the reaction rates. A possible method of synthesizing such a system in a wet lab is explained in more detail. Finally, stability results indicate the possibility of stabilizing an unstable system with added delayed feedbacks (by adding larger delays). This approach may also be applicable to systems with large delays in which simple controllers are needed due to limitations in computational power. This paper motivates and provides preliminary results towards direct design of purely delay based controllers for network systems with large delays.ers for network systems with large delays.  +
• This paper proposes a method to determine … This paper proposes a method to determine trajectories of dynamic systems that steer</br>between two end points while satisfying linear inequality constraints arising from limits</br>on states and inputs. The method exploits the structure of the dynamic system written in a</br>higher-order form to explicitly eliminate the state equations. The feasible trajectories</br>of the dynamic system are sought within a characterization with a finite sum of mode</br>functions. In this paper, the linear inequalities on inputs and states are replaced by a</br>finite set of linear inequalities on the mode coefficients. This step changes the problem</br>of trajectory generation into finding a convex polytope enclosed by the linear</br>inequalities on the mode coefficients. A procedure is then developed to efficiently find</br>the vertices of this bounding polytope. It is demonstrated in this paper that this method</br>can generate feasible trajectories of the system in real-time and can quickly update the</br>trajectories as the terminal conditions are changed. The procedure is demonstrated</br>numerically by two examples. The results of one of the examples is implemented in hardware</br>to explore the issues of real-time planning and control. issues of real-time planning and control.  +
• This paper proposes a new synthetic in vit … This paper proposes a new synthetic in vitro circuit that aims at regulating the rate of RNA transcription through positive feedback interactions. This design is dual to a previously synthesized transcriptional rate regulator based on self-repression. Two DNA templates are designed to interact through their transcripts, creating cross activating feedback loops that will equate their transcription rates at steady state. A mathematical model is developed for this circuit, consisting of a set of ODEs derived from the mass action laws and Michaelis--Menten kinetics involving all the present chemical species. This circuit is then compared to its regulatory counterpart based on negative feedback. A global sensitivity analysis reveals the fundamental features of the two designs, by evaluating their equilibrium response to changes in the most crucial parameters of the system.the most crucial parameters of the system.  +
• This paper proposes a real-time planning s … This paper proposes a real-time planning scheme and its implementation for a class of dynamic systems. The planner is aimed to satisfy the state equations, the path and actuator constriants, and the given initial and terminal constraints. In order to generate trajectories in real-time, three broad steps are performed: (1) the structure of differentially flat systems is used to explicitly encapsulate the state equations into linear differential constraints in a flat space, and appropriately transform the boundary conditions; (ii) using semi-infinite optimization theory, an inner approximation of nonlinear constraints is made to replace these by a set of linear inequalities in the flat space, i.e., by a polytope; (iii) this polytopic representation of the system that satisfies the state equations and the constraints is then parameterized using basis functions and the planning problem is turned around into solution of a set of linear inequalities in the coefficient space of the basis functions. It is then demonstrated that numerically efficient algorithms can be built to solve the planning problem in real-time. The essence of the approach is demonstrated by two examples: (1) an implementation is performed on a spring-mass-damper system to demonstrate the real-time capability of evasion-pursuit; (ii) a VTOL aircraft is used to illustrate the application of this approach in simulation to nonlinear problems.roach in simulation to nonlinear problems.  +
• This paper proposes a set-based parameter … 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.ems and a generalized bisection algorithm.  +
• This paper proposes an intuitive nonlinear … This paper proposes an intuitive nonlinear lateral control strategy for trajectory tracking in autonomous </br>nonholonomic vehicles. The controller has been implemented and verified in Alice, Team Caltech's contribution to the 2007 DARPA Urban Challenge competition for autonomous </br>motorcars. A kinematic model is derived. The control law is described and analyzed. Results from simulations and field tests are given and evaluated. Finally, the key features of the proposed controller are reviewed, followed by a discussion of some limitations of the proposed strategy.some limitations of the proposed strategy.  +
• This paper proposes two new metrics to eva … This paper proposes two new metrics to evalu- ate learned object detection models for quantitative system-level analysis via probabilistic model-checking. In particular, proposition-labeled and distance-parametrized confusion matrices are defined for evaluating object detection, and these metrics are leveraged to compute the probability of the closed- loop system satisfying its system-level formal specifications. Instead of using object class labels, the proposition-labeled confusion matrix uses atomic propositions relevant to the high- level planning strategy. Furthermore, unlike the traditional confusion matrix, the distance-parametrized confusion matrix accounts for variations in detection performance with respect to the distance between the ego and the object. We empirically show that these evaluation metrics chosen with the context of i) system-level specifications and ii) the planning module lead to a less conservative analysis in comparison to canonical metrics that do not take these into account. We demonstrate this framework on a discrete-state car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic (LTL).formalized in Linear Temporal Logic (LTL).  +
• This paper provides a theoretical framewor … This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations.rative control of multivehicle formations.  +
• This paper provides analytical results reg … This paper provides analytical results regarding the stability of linear discrete-time systems with stochastic delays. Necessary and sufficient stability conditions are derived by using the second moment dynamics which can be used to draw stability charts. The results are applied to a simple connected vehicle system where the stability regions are com- pared to those given by the mean dynamics. Our results reveal some fundamental limitations of connected cruise control which becomes more significant as the packet drop ratio increases.ficant as the packet drop ratio increases.  +
• This paper provides preliminary work in an … This paper provides preliminary work in an aim to fundamentally understand the effects of temperature fluctuations in the dynamics of biological oscillators. Motivated by circadian rhythms, we are interested in understanding how time-varying temperatures might play a role in the properties of biochemical oscillators. This paper investigates time-dependent Arrhenius scaling of biochemical networks with delays. We assume these time-delays arise from a sequence of simpler reactions that can be modeled as an aggregate delay. We focus on a model system, the Goodwin oscillator, in which we use time-varying rate coefficients as a mechanism to understand the possible effects of temperature fluctuations. The emergence of delays from a sequence of reactions can be better understood through the Goodwin model. For a high order system and comparably high reaction rates, one can approximate the large sequence of reactions in the model with a delay, which can be interpreted as the time needed to go through the âqueueâ. Such types of delays can arise in the process of transcription for example. To study how these delays are affected by temperature fluctuations, we take the limit as the order of the system and the mean reaction rates approach infinity with a periodically time-varying rate coefficient. We show that the limit cycle of the Goodwin oscillator varies only in the limit when the oscillator frequency is much larger than the frequency of temperature oscillations. Otherwise, the instantaneous frequency of the oscillator is dominated by the mean value of the time-varying temperature.ean value of the time-varying temperature.  +
• This paper studies the evaluation of learn … This paper studies the evaluation of learning- based object detection models in conjunction with model-checking of formal specifications defined on an abstract model of an autonomous system and its environment. In particular, we define two metrics – proposition-labeled and class-labeled confusion matrices – for evaluating object detection, and we incorporate these metrics to compute the satisfaction probability of system-level safety requirements. While confusion matrices have been effective for comparative evaluation of classification and object detection models, our framework fills two key gaps. First, we relate the performance of object detection to formal requirements defined over downstream high-level planning tasks. In particular, we provide empirical results that show that the choice of a good object detection algorithm, with respect to formal requirements on the overall system, significantly depends on the downstream planning and control design. Secondly, unlike the traditional confusion matrix, our metrics account for variations in performance with respect to the distance between the ego and the object being detected. We demonstrate this framework on a car-pedestrian example by computing the satisfaction probabilities for safety requirements formalized in Linear Temporal Logic (LTL).formalized in Linear Temporal Logic (LTL).  +
• This paper summarizes the findings and rec … This paper summarizes the findings and recommendations of a recent panel on</br>Future Directions in Control, Dynamics, and Systems, sponsored by the US Air</br>Force Office of Scientific Research. A set of grand challenges that</br>illustrate some of the recommendations and opportunities are provided.</br>Finally, the paper describes two new courses being developed at Caltech that</br>are aligned with the recommendations of the report.ed with the recommendations of the report.  +
• This report describes Team Caltech's techn … This report describes Team Caltech's technical approach and results for the 2007 DARPA Urban Challenge. Our primary technical thrusts were in three areas: (1) mission and contingency management for autonomous systems; (2) distributed sensor fusion, mapping and situational awareness; and (3) optimization-based guidance, navigation and control. Our autonomous vehicle, Alice, demonstrated new capabiliites in each of these areas and drove approximately 300 autonomous miles in preparation for the race. The vehicle completed 2 of the 3 qualification tests, but did not ultimately qualify for the race due to poor performance in the merging tests at the National Qualifying </br>Event.g tests at the National Qualifying Event.  +
• This report explores the tradeoffs and lim … This report explores the tradeoffs and limits of performance in feedback control of interconnected multi-agent systems, focused on the network sensitivity functions. We consider the interaction topology described by a directed graph and we prove that the sensitivity transfer functions between every pair of agents, arbitrarily connected, can be derived using a version of the Mason's Direct Rule. Explicit forms for special types of graphs are presented. An analysis of the role of cycles points out that these structures influence and limit considerably the performance of the system. The more the cycles are equally distributed among the formation, the better performance the system can achieve, but they are always worse than the single agent case. We also prove the networked version of Bode's integral formula, showing that it still holds for multi-agent systems.at it still holds for multi-agent systems.  +
• This report presents techniques for using … This report presents techniques for using discrete finite</br>rotations to reorient a spacecraft from a given initial attitude to a</br>final attitude which satisfies a specified aiming objective. The</br>objective may be a fully specified final orientation or it may require</br>that the spacecraft direct an instrument along a certain</br>direction. Constraints are also imposed on the allowable intermediate</br>orientations that the spacecraft may assume during the course of the</br>maneuver, representing the operational requirements of onboard</br>instrumentation. The algorithms presented consider solutions that</br>will achieve the desired objective with only one or two slew</br>maneuvers, although they may be easily extended to consider more</br>complicated solutions requiring additional maneuvers. solutions requiring additional maneuvers.  +
• This research addresses the path planning … This research addresses the path planning problem</br>with a nonlinear optimization method running in real</br>time. An optimization problem is continually solved to find a</br>time-optimal, dynamically feasible trajectory from the vehicleâs</br>position to some receding horizon ahead (20m-70m forward).</br>The locally optimal numerical solver optimizes both the spatial</br>and temporal components of the trajectory simultaneously, and</br>feeds its output to a trajectory-following controller. The method</br>has been implemented and tested on a modified Ford E350</br>van. Using one stereo pair and four LADAR units as terrain</br>sensors, the vehicle was able to consistently traverse a 2 mile</br>obstacle course at the DGC qualifying event. At the main</br>DGC event, the vehicle drove 8 autonomous miles through the</br>Nevada desert before experiencing non-planning issues. During</br>this time, the planning system generated a plan 4.28 times</br>per second on average. This execution speed, coupled with a</br>feedback-based trajectory-following controller was shown to be</br>adequate at providing smooth and reliable obstacle avoidance</br>even on complicated terrain.cle avoidance even on complicated terrain.  +
• This survey aims to provide a general over … This survey aims to provide a general overview of relevant terms and resources for understanding the intersection of synthetic biology and control theory. A reader with a background in control theory should come away with a reasonable understanding of the current 24 state-of-the-art of biological system identification, controller design and implementation, and the open challenges facing the field. Additionally, this review updates and builds upon previous publications on this subject. As this particular work is limited to a selected number of topics, additional reviews are suggested throughout the text for deeper reading. In the following sections, each of the challenges is addressed within the typical workflow for control implementation of more traditionally engineered systems (Figure 1). Engineered biological systems present a number of challenges to all stages of this workflow for reasons such as limitations in real-time measurement, resource competition with the host organism, and incomplete knowledge of underlying biological processes. First, strategies for framing a biologi- cal organism as a system with defined inputs, outputs, sensors, actuators, and measurements are discussed (Figure 1a). Obtaining dynamic and reliable measurements within biological organisms is a daunting challenge, engineered or otherwise. An overview of the state-of-the-art tools for modeling and characterizing biological systems is presented, followed by system identification methods specifically designed for the types of data available from biological measurements. The difficulty in engineering complex genetic networks, combined with severe limitations in real- time measurement, means that the body of work for controller design (Figure 1b) is limited – as a result, we discuss the open problems and challenges awaiting the entrepreneurial reader, and also present a number of examples of feedback loop implementation in living cells (Figure 1c). Finally, the necessary challenges in synthetic biology and development of control theoretical frameworks that need to be addressed in order to advance the field are discussed. order to advance the field are discussed.  +
• This thesis addresses the problem of estim … This thesis addresses the problem of estimating the state in multi-agent decision and </br>control systems. In particular, a novel approach to state estimation is developed that uses </br>partial order theory in order to overcome some of the severe computational complexity </br>issues arising in multi-agent systems. Within this approach, state estimation algorithms are </br>developed, which enjoy proved convergence properties and are scalable with the number </br>of agents. </br><p></br>The dynamic evolution of the systems under study are characterized by the interplay of </br>continuous and discrete variables. Continuous variables usually represent physical quan- </br>tities such as position, velocity, voltage, and current, while the discrete variables usually </br>represent quantities internal to the decision protocol that is used for coordination, com- </br>munication, and control. Within the proposed state estimation approach, the estimation of </br>continuous and discrete variables is developed in the same mathematical framework, as a </br>joint continuous-discrete space is considered for the estimator. This way, the dichotomy </br>between the continuous and discrete world is overcome for the purpose of state estimation. </br><p></br>Application examples are considered, which include the state estimation in competi- </br>tive multi-robot systems and in multi-agent discrete event systems, and the monitoring of </br>distributed environments.tems, and the monitoring of distributed environments.  +
• This thesis explores the paradigm of two d … This thesis explores the paradigm of two degree of freedom design for</br>nonlinear control systems. In two degree of freedom design one</br>generates an explicit trajectory for state and input around which the</br>system is linearized. Linear techniques are then used to stabilize the</br>system around the nominal trajectory and to deal with</br>uncertainty. This approach allows the use of the wealth of tools in</br>linear control theory to stabilize a system in the face of</br>uncertainty, while exploiting the nonlinearities to increase</br>performance. Indeed, this thesis shows through simulations and</br>experiments that the generation of a nominal trajectory allows more</br>aggressive tracking in mechanical systems.</br><p></br>The generation of trajectories for general systems involves the</br>solution of two point boundary value problems which are hard to solve</br>numerically. For the special class of differentially flat systems</br>there exists a unique correspondence between trajectories in the</br>output space and the full state and input space. This allows us to</br>generate trajectories in the lower dimensional output space where we</br>don't have differential constraints, and subsequently map these to the</br>full state and input space through an algebraic procedure. No</br>differential equations have to be solved in this process. This thesis</br>gives a definition of differential flatness in terms of differential</br>geometry, and proves some properties of flat systems. In particular,</br>it is shown that differential flatness is equivalent to dynamic</br>feedback linearizability in an open and dense set.</br><p></br>This dissertation focuses on differentially flat systems. We describe</br>some interesting trajectory generation problems for these systems, and</br>present software to solve them. We also present algorithms and</br>software for real time trajectory generation, that allow a</br>computational tradeoff between stability and performance. We prove</br>convergence for a rather general class of desired trajectories. If a</br>system is not differentially flat we can approximate it with a</br>differentially flat system, and extend the techniques for flat</br>systems. The various extensions for approximately flat systems are</br>validated in simulation and experiments on a thrust vectored</br>aircraft. A system may exhibit a two layer structure where the outer</br>layer is a flat system, and the inner system is not. We call this</br>structure \emph{outer flatness}. We investigate trajectory generation</br>for these systems and present theorems on the type of tracking we can</br>achieve. We validate the outer flatness approach on a model helicopter</br>in simulations and experiment.h on a model helicopter in simulations and experiment.  +
• This thesis focuses on understanding the u … This thesis focuses on understanding the use of air injection as a </br>means of controlling rotating stall in an axial flow compressor, </br>involving modeling, dynamical systems analysis, and experimental </br>investigations.</br><p></br>The first step towards this understanding was the development </br>of a low order model for air injection control, the starting point of </br>which was the Moore and Greitzer model for axial flow compressors. The </br>Moore and Greitzer model was extended to include the effects of air </br>injection and bifurcation analysis was performed to determine how the closed </br>loop system dynamics are different from those of the open loop system. </br>This low order model was then used to determine the optimal placement of </br>the air injection actuators.</br><p></br>Experimental work focused on verifying that the low order model,</br>developed for air injection actuation, qualitatively captured the</br>behavior of the Caltech compressor rig. Open loop tests were performed</br>to determine how the placement of the air injectors on the rig</br>affected the performance of the compressor. The positioning of the air</br>injectors that provided the greatest control authority were used in</br>the development of air injection controllers for rotating stall. The</br>controllers resulted in complete elimination of the hysteresis</br>associated with rotating stall. The use of a throttle actuator for the</br>control of the surge dynamics was investigated, and then combined with</br>an air injection controller for rotating stall; the resulting</br>controller performed quite well in throttle disturbance rejection</br>tests.</br><p></br>A higher order model was developed to qualitatively match the</br>experimental results with a simulation. The results of this modeling</br>effort compared quite well with the experimental results for the open</br>loop behavior of the Caltech rig. The details of how the air injection</br>actuators affect the compressor flow were included in this model, and</br>the simulation predicted the same optimal controller that was</br>developed through experimentation.</br><p></br>The development of the higher order model also included the </br>investigation of systematic methods for determining the simulation parameters. </br>Based on experimental measurements of compression system transients, the </br>open loop simulation parameters were identified, including values for </br>the compressor performance characteristic in regions where direct </br>measurements were not possible. These methods also provided information on </br>parameters used in the modeling of the pressure rise delivered by the </br>compressor under unsteady flow conditions.</br><p>e delivered by the compressor under unsteady flow conditions. <p>  +
• This tutorial describes TuLiP, the Tempora … This tutorial describes TuLiP, the Temporal Logic Planning toolbox, a collection of tools for designing controllers</br>for hybrid systems from specifications in temporal logic. The</br>tools support a workflow that starts from a description of</br>desired behavior, and of the system to be controlled. The</br>system can have discrete state, or be a hybrid dynamical</br>system with a mixed discrete and continuous state space. The</br>desired behavior can be represented with temporal logic and</br>discrete transition systems. The system description can include</br>uncontrollable variables that take discrete or continuous values,</br>and represent disturbances and other environmental factors</br>that affect the dynamics, as well as communication signals that</br>affect controller decisions.</br></br>A control design problem is solved in phases that involve</br>abstraction, discrete synthesis, and continuous feedback control.</br>Abstraction yields a discrete description of system dynamics in</br>logic. For piecewise affine dynamical systems, this abstraction</br>is constructed automatically, guided by the geometry of the dynamics</br>and under logical constraints from the specification. The</br>resulting logic formulae describe admissible discrete behaviors</br>that capture both controlled and environment variables. The</br>discrete description resulting from abstraction is then conjoined</br>with the desired logic specification. To find a controller, the</br>toolbox solves a game of infinite duration. Existence of a discrete</br>(winning) strategy for the controlled variables in this game is a</br>proof certificate for the existence of a controller for the original</br>problem, which guarantees satisfaction of the specification. This</br>discrete strategy, concretized by using continuous controllers,</br>yields a feedback controller for the original hybrid system. The</br>toolbox frontend is written in Python, with backends in C,</br>Python, and Cython.</br></br>The tutorial starts with an overview of the theory behind</br>TuLiP, and of its software architecture, organized into specifi-</br>cation frontends and backends that implement algorithms for</br>abstraction, solving games, and interfaces to other tools. Then,</br>the main elements for writing a specification for input to TuLiP</br>are introduced. These include logic formulae, discrete transition</br>systems annotated with predicates, and hybrid dynamical systems,</br>with linear or piecewise affine continuous dynamics. The</br>working principles of the algorithms for predicate abstraction</br>and discrete game solving using nested fixpoints are explained,</br>by following the input specification through the various transformations</br>that compile it to a symbolic representation that</br>scales well to solving large games. The tutorial concludes</br>with several design examples that demonstrate the toolbox’s</br>capabilities.at demonstrate the toolbox’s capabilities.  +
• This work develops the geometry and dynami … This work develops the geometry and dynamics of mechanical systems with nonholonomic</br>constraints and symmetry from the perspective of Lagrangian mechanics and with a view to</br>control theoretical applications. The basic methodology is that of geometric mechanics</br>applied to the formulation of Lagrange d'Alembert, generalizing the use of connections and</br>momentum maps associated with a given symmetry group to this case. We begin by formulating</br>the mechanics of nonholonomic systems using an Ehresmann connection to model the</br>constraints, and show how the curvature of this connection enters into Lagrange's</br>equations. Unlike the situation with standard configuration space constraints, the</br>presence of symmetries in the nonholonomic case may or may not lead to conservation laws.</br>However, the momentum map determined by the symmetry group still satisfies a useful</br>differential equation that decouples from the group variables. This momentum equation,</br>which plays an important role in control problems, involves parallel transport operators</br>and is computed explicitly in coordinates. An alternative description using a ``body</br>reference frame'' relates part of the momentum equation to the components of the</br>Euler-Poincar\'{e} equations along those symmetry directions consistent with the</br>constraints. One of the purposes of this paper is to derive this evolution equation for</br>the momentum and to distinguish geometrically and mechanically the cases where it is</br>conserved and those where it is not. An example of the former is a ball or vertical disk</br>rolling on a flat plane and an example of the latter is the snakeboard, a modified version</br>of the skateboard which uses momentum coupling for locomotion generation. We construct a</br>synthesis of the mechanical connection and the Ehresmann connection defining the</br>constraints, obtaining an important new object we call the nonholonomic connection. When</br>the nonholonomic connection is a principal connection for the given symmetry group, we</br>show how to perform Lagrangian reduction in the presence of nonholonomic constraints,</br>generalizing previous results which only held in special cases. Several detailed examples</br>are given to illustrate the theory.amples are given to illustrate the theory.  +
• This work discusses feasibility aspects of … This work discusses feasibility aspects of motion planning for</br>groups of agents connected by a range-constrained wireless</br>network. Specifically, we address the difficulties encountered</br>when trajectories are required to preserve the connectedness of</br>the network. The analysis utilizes a quantity called the</br>connectivity robustness of the network, which can be</br>calculated in a distributed fashion, and thus is applicable to</br>distributed motion planning problems arising in control of vehicle</br>networks. Further, these results show that network constraints</br>posed as connectivity robustness constraints have minimal impact</br>on reachability, provided that an appropriate topology control</br>algorithm is implemented. This contrasts with more naive</br>approaches to connectivity maintenance, which can significantly</br>reduce the reachable set.an significantly reduce the reachable set.  +
• This work examines several dynamical aspec … This work examines several dynamical aspects of average consensus</br>in mobile networks. The results herein allow consensus on general</br>time-varying signals, and allow tracking analysis using standard</br>frequency-domain techniques. Further, the frequency-domain</br>analysis naturally inspires a robust small-gain version of the</br>algorithm, which tolerates arbitrary non-uniform time delays.</br>Finally, we show how to exploit a dynamical conservation property</br>in order to ensure consensus tracking despite splitting and</br>merging of the underlying mobile network. merging of the underlying mobile network.  +
• This work illuminates a theory of locomoti … This work illuminates a theory of locomotion rooted in geometric</br> mechanics and nonlinear control. We regard the internal configuration</br> of a deformable body, together with its position and orientation in</br> ambient space, as a point in a trivial principal fiber bundle over the</br> manifold of body deformations. We obtain connections on such bundles</br> which describe the nonholonomic constraints, conservation laws, and</br> force balances to which certain propulsors are subject, and construct</br> and analyze control-affine normal forms for different classes of</br> systems. We examine the applicability of results involving geometric</br> phases to the practical computation of trajectories for systems</br> described by single connections. We propose a model for planar</br> carangiform swimming based on reduced Euler-Lagrange equations for the</br> interaction of a rigid body and an incompressible fluid, accounting</br> for the generation of thrust due to vortex shedding through controlled</br> coupling terms. We investigate the correct form of this coupling</br> experimentally with a robotic propulsor, comparing its observed</br>behavior with that predicted numerically. behavior with that predicted numerically.  +
• This work is an extension to a companion p … This work is an extension to a companion paper describing</br>consensus-tracking for networked agents, and shows how those</br>results can be applied to obtain least-squares fused estimates</br>based on spatially distributed measurements. This mechanism is</br>very robust to changes in the underlying network topology and</br>performance, making it an interesting candidate for sensor fusion</br>on autonomous mobile networks. We conclude with an example of a</br>preliminary application to distributed Kalman Filtering using the</br>proposed technique, illustrating the dependence of the performance</br>on the structure of the underlying network.n the structure of the underlying network.  +
• This work is motivated by the problem of s … This work is motivated by the problem of synthe- sizing mode sequences for continuous-time polynomial switched systems in order to guarantee that the trajectories of the system satisfy certain high-level specifications expressed in linear temporal logic. We use augmented finite transition systems as abstract models of continuous switched systems. Augmented finite transition systems are equipped with liveness properties that can be used to enforce progress in accordance with the underlying dynamics. We then introduce abstraction and refinement relations that induce a preorder on this class of finite transition systems. By construction, the resulting pre-order respects the feasibility (i.e., realizability) of the synthesis problem. Hence, existence of a discrete switching strategy for one of these abstract finite transition systems guarantees the existence of a mode sequence for the continuous system such that all of its trajectories satisfy the specification. We also present an algorithm, which can be implemented using sum-of-squares based relaxations, to compute such high fidelity abstract models in a computationally tractable way. Finally, these ideas are illustrated on an example.these ideas are illustrated on an example.  +
• This work proposes a language for describi … This work proposes a language for describing reactive synthesis problems that integrates imperative and declarative elements. The semantics is defined in terms of two-player turn-based infinite games with full information. Currently, synthesis tools accept linear temporal logic (LTL) as input, but this description is less structured and does not facilitate the expression of sequential constraints. This motivates the use of a structured programming language to specify synthesis problems. Transition systems and guarded commands serve as imperative constructs, expressed in a syntax based on that of the modeling language Promela. The syntax allows defining which player controls data and control flow, and separating a program into assumptions and guarantees. These notions are necessary for input to game solvers. The integration of imperative and declarative paradigms allows using the paradigm that is most appropriate for expressing each requirement. The declarative part is expressed in the LTL fragment of generalized reactivity(1), which admits efficient synthesis algorithms. The implementation translates Promela to input for the Slugs synthesizer and is written in Python.lugs synthesizer and is written in Python.  +
• This work proposes a symbolic algorithm fo … This work proposes a symbolic algorithm for the construction of assume-guarantee specifications that allow multiple agents to coop- erate. Each agent is assigned goals expressed in a fragment of linear temporal logic known as gener- alized Streett with one pair, GR(1). These goals may be unrealizable, unless each agent makes additional assumptions, about the behavior of other agents. The algorithm constructs a con- tract among the agents, in that only the infinite behavior of the given goals is constrained, known as liveness, not the finite one, known as safety. This defers synthesis to a later stage of refinement, modularizing the design process. We prove that there exist GR(1) games that do not admit any GR(1) contract. For this reason, we formulate contracts with nested GR(1) properties and auxiliary communication variables, and prove that they always exist. The algorithmâs fixpoint structure is similar to GR(1) synthesis, enjoying time complexity polynomial in the number of states, and linear in number of recurrence goals. and linear in number of recurrence goals.  +
• To contribute to efforts of bringing forma … 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.of a networked control systems of traffic.  +
• Traditional feedback control systems give … Traditional feedback control systems give little attention to issues associated with the flow of information through the feedback loop. Typically implemented with dedicated communication links that deliver nearly precise, reliable, and non-delayed information, researchers have not needed to concern themselves with issues related to quantized, delayed, and even lost information. With the advent of newer technologies and application areas that pass information through non-reliable networks, these issues cannot be ignored. In recent years the field of Networked Control Systems (NCS) has emerged to describe situations where these issues are present. The research in this field focuses on quantifying performance degradations in the presence of network effects and proposing algorithms for managing the information flow to counter those negative effects. In this thesis I propose and analyze algorithms for managing information flow for several Networked Control Systems scenarios: state estimation with lossy measurement signals, using input buffers to reduce the frequency of communication with a remote plant, and performing state estimation when control signals are transmitted to a remote plant via a lossy communication link with no acknowledgement signal at the estimator. Multi-agent coordinated control systems serve as a prime example of an emerging area of feedback control systems that utilize feedback loops with information passed through possibly imperfect communication networks. In these systems, agents use a communication network to exchange information in order to achieve a desired global ob jective. Hence, managing the information flow has a direct impact on the performance of the system. I also explore this area by focusing on the problem of multi-agent average consensus. I propose an algorithm based on a hierarchical decomposition of the communication topology to speed up the time to convergence. For all these topics I focus on designing intuitive algorithms that intelligently manage the information flow and provide analysis and simulations to illustrate their effectiveness.lations to illustrate their effectiveness.  +
• Using geometric concepts from observabilit … Using geometric concepts from observability theory for nonlinear </br>systems, we propose an approach for parameter estimation for linearly and </br>nonlinearly parameterized systems that does not rely on persistence of </br>excitation conditions. The proposed approach relies on extending a </br>parameter estimation problem to a state estimation problem by introducing </br>the parameters as auxiliary state variables. Applying tools from geometric </br>nonlinear control theory we give an observability check for parameters, </br>and, in case the parameters are observable, we provide a constructive way </br>to design a local parameter observer with established speed of </br>convergence.er with established speed of convergence.  +
• Using tools from dynamical systems and sys … Using tools from dynamical systems and</br>systems identification we develop a framework for the study of </br>decomposition of</br>human motion. The objective is understanding human motion by decomposing </br>it into a sequence of elementary building blocks, which we refer to as </br>movemes, that belong to a known alphabet of dynamical </br>systems.</br>We develop classification and segmentation algorithms with error analysis </br>and we test them on human drawing data.s and we test them on human drawing data.  +
• Using tools from dynamical systems and sys … Using tools from dynamical systems and systems identification we develop a framework for the study</br>of primitives for human motion, which we refer to as movemes. The objective is understanding human</br>motion by decomposing it into a sequence of elementary building blocks that belong to a known alphabet</br>of dynamical systems. In this work we address the problem of defining conditions under which</br>collections of signals are well-posed according to a dynamical model class M and then can generate</br>movemes. Based on the assumption of well-posedness, we develop segmentation and classification algorithms</br>in order to reduce a complex activity into the sequence of movemes that have generated it.</br>Using examples we show that the definition of well-posedness can be applied in practice and show</br>analytically that the proposed algorithms are robust with respect to noise and model uncertainty. We</br>test our ideas on data sampled from five human subjects who were drawing figures using a computer</br>mouse. Our experiments show that we are able to distinguish between movemes and recognize them</br>even when they take place in activities containing more than one moveme at a time.  +
• Using tools from dynamical systems theory … Using tools from dynamical systems theory and systems identification theory </br>we develop the study of primitives for human motion which we refer to as <i>movemes</i>. We </br>introduce basic definitions of dynamical independence of LTI systems and segmentability of </br>signals and, for two dimensional motions, we develop classification and segmentation algorithms. </br>We test our ideas on data sampled from four human subjects who were engaged in a </br>simple real-life activity including two movemes. Our experiments show that we are able to </br>distinguish between the two movemes and recognise them even when they take place in an </br>activity containing more than one moveme.place in an activity containing more than one moveme.  +
• Vehicles in formation often lack global in … Vehicles in formation often lack global information regarding the state of</br>all the vehicles, a deficiency which can lead to instability and poor performance. In</br>this paper, we demonstrate how exchange of minimal amounts of information between</br>vehicles can be designed to realize a dynamical system which supplies each vehicle with</br>a shared reference trajectory. When the information flow law is placed in the control</br>loop, a separation principle is proven which guarantees stability of the formation and</br>convergence of the information flow law regardless of the information flow topology.gardless of the information flow topology.  +
• We address the problem of estimating discr … We address the problem of estimating discrete variables in a class of deterministic</br>transition systems where the continuous variables are available for measurement. This</br>simplified scenario has practical interest, for example, in the case of decentralized multi-robot</br>systems. In these systems, the continuous variables represent physical quantities such as the</br>position and velocity of a robot, while discrete variables may represent the state of the logical</br>system that is used for control and coordination. We propose a novel approach to the</br>estimation of discrete variables using basic lattice theory that overcomes some of the severe</br>complexity issues encountered in previous work. We show how to construct the proposed</br>estimator for a multi-robot system performing a cooperative assignment task. performing a cooperative assignment task.  +
• We analyze a jump linear Markov system bei … We analyze a jump linear Markov system being stabilized using a zero-order hold controller. We consider the case when the Markov state is associated with the probability distribution of a measured variable. We assume that the Markov state is not known, but rather is being estimated based on the observations of the variable. We present conditions for the stability of such a system and also solve the optimal LQR control problem for the case when the state estimate update uses only the last observation value. In particular we consider a suboptimal causal version of the Viterbi estimation algorithm and show that a separtion property does not hold between the optimal control and the Markov state estimate. Some simple examples are also presented.. Some simple examples are also presented.  +
• We analyze a network of dynamic agents whe … We analyze a network of dynamic agents where the</br>topology of the network specifies the information</br>flow between the agents. We present an analysis</br>method for such a system for both consensus and</br>formation stabilization problems. We consider the</br>case of agent dynamics being a single integrator in</br>more detail to show the general features introduced</br>by the information flow. Then we show that the</br>method of analysis can be extended to more general cases of complicated agent dynamics, non-ideal</br>links for information flow, etc. We also consider the</br>case when the topology of the network is changing</br>over time. The focus of the paper is on obtaining</br>conditions for the stability of the formation that</br>can be checked in a decentralized way. Some simple examples are also presented.. Some simple examples are also presented.  +
• We analyze the performance of an approxima … We analyze the performance of an approximate distributed Kalman filter proposed</br>in recent work on distributed coordination. This approach to</br>distributed estimation is novel in that it admits a systematic</br>analysis of its performance as various network quantities such as</br>connection density, topology, and bandwidth are varied. Our main</br>contribution is a frequency-domain characterization of the</br>distributed estimator's steady-state performance; this is quantified in terms</br>of a special matrix associated with the connection topology called</br>the graph Laplacian, and also the rate of message exchange</br>between immediate neighbors in the communication network.te neighbors in the communication network.  +
• We consider a discrete time linear feedbac … We consider a discrete time linear feedback control system with additive noise where the control signals are </br>to be sent across a data link from the controller to the actuators. Due to network constraints it is desired to reduce the transmission frequency of the control signals. We show that by </br>including a finite sequence of predicted control signals in each </br>communication packet the frequency of transmission can be reduced by transmitting only when the previously sent sequence has run out. The price to pay is that the closed loop error </br>will increase. We introduce a novel communication protocol, which we call Input Difference Transmission Scheme (IDTS), which transmits control packets when the difference between the newly computed control sequence and the predicted control </br>sequence previously transmitted is larger than a certain thresh- </br>old. This threshold is a design parameter and we show how </br>the closed loop behavior varies with this threshold. Simulation </br>results are provided to augment the theory and show how the </br>protocol works.e theory and show how the protocol works.  +
• We consider a network of identical agents … We consider a network of identical agents with arbitrary linear time-invariant (LTI) dynamics such that the network reaches consensus asymptotically. Uniform time delay is taken into account in the communication channels. The goal of this paper is to maximize the delay (so-called delay margin) that the system can tolerate before becoming unstable by implementing a low-order controller to a single agent. A parametric design method is investigated to guarantee the stability and consensusability. The set of all feasible low-order controllers based on the frequency response data is characterized by combining the argument principle and the generalized Nyquist criterion. Based on this, the algorithm of computing the delay margin is proposed for a given controlled agent. By combining all the possible margins for each controlled agent, we then can obtain the maximal delay margin for the whole network and the corresponding local controller.rk and the corresponding local controller.  +
• We consider identifiability of linear syst … We consider identifiability of linear systems driven by white noise using a combination of distributional and time series measurements. Specifically, we assume that the system has no control inputs available and can only be observed at stationarity. The user is able to measure the full stationary state distribution as well as observe time correlations for small subsets of the state. We formulate theoretical conditions on identifiability of parameters from distributional information alone. We then give a sufficient condition and an effective necessary condition for identifiability using a combination of distributional and time series measurements. We illustrate the ideas with some simple examples as well as a biologically inspired example of a transcription and degradation process.f a transcription and degradation process.  +
• We consider mobile robot navigation in den … We consider mobile robot navigation in dense human crowds. In particular, we explore two questions. Can we design a navigation algorithm that encourages humans to coop- erate with a robot? Would such cooperation improve navigation performance? We address the first question by developing a probabilistic predictive model of cooperative collision avoidance and goal-oriented behavior. Specifically, this model extends the recently introduced interacting Gaussian processes approach to the case of multiple goals and stochastic movement duration. We answer the second question by empirically validating our model in a natural environment (a university cafeteria), and in the process, carry out the first extensive quantitative study of robot navigation in dense human crowds (completing 488 runs). The âmultiple goalâ interacting Gaussian processes algorithm performs comparably with human teleoperators in crowd densities near 1 person/m2, while a state of the art noncooperative planner exhibits unsafe behavior more than 3 times as often as our planner. Furthermore, a reactive planner based on the âdynamic windowâ approachâwidely used for robotic tour guide experimentsâfails for crowd densities above 0.55 people/m2. We conclude that a cooperation model is critical for safe and efficient robot navigation in dense human crowds.nt robot navigation in dense human crowds.  +
• We consider optimal control for a system s … We consider optimal control for a system subject to temporal logic constraints. We minimize a weighted average cost function that generalizes the commonly used average cost function from discrete-time optimal control. Dynamic programming algorithms are used to construct an optimal trajectory for the system that minimizes the cost function while satisfying a temporal logic specification. Constructing an optimal trajectory takes only polynomially more time than constructing a feasible trajectory. We demonstrate our methods on simulations of autonomous driving and robotic surveillance tasks.us driving and robotic surveillance tasks.  +
• We consider the bootstrapping problem, whi … We consider the bootstrapping problem, which consists in learning a model of the agent's sensors and actuators starting from zero prior informa- tion, and we take the problem of servoing as a cross-modal task to validate the learned models. We study the class of sensors with bilinear dynamics, for which the derivative of the observations is a bilinear form of the control commands and the observations themselves. This class of models is simple, yet general enough to represent the main phenomena of three representative sensors (field sampler, camera, and range-finder), apparently very different from one another. It also allows a bootstrapping algorithm based on Hebbian learning, and a simple bioplausible control strategy. The convergence proper- ties of learning and control are demonstrated with extensive simulations and by analytical arguments.e simulations and by analytical arguments.  +
• We consider the control of dynamically dec … We consider the control of dynamically decoupled</br>subsystems whose state vectors are coupled in the cost</br>function of a finite horizon optimal control problem. For a</br>given cost structure, we generate distributed optimal control</br>problems for each subsystem and establish that a distributed</br>receding horizon implementation is asymptotically stabilizing.</br>The communication requirements at each receding</br>horizon update include the exchange of the previous optimal</br>control trajectory between subsystems with coupling in</br>the cost function. The key requirements for stability are that</br>each distributed optimal control not deviate too far from the</br>previous one, and that the receding horizon updates happen</br>sufficiently fast. A simulation example of multi-vehicle</br>formation stabilization is provided.hicle formation stabilization is provided.  +
• We consider the control of interacting sub … We consider the control of interacting subsystems whose dynamics and constraints</br>are uncoupled, but whose state vectors are coupled non-separably in a single centralized</br>cost function of a finite horizon optimal control problem. For a given centralized</br>cost structure, we generate distributed optimal control problems for each subsystem</br>and establish that the distributed receding horizon implementation is asymptotically</br>stabilizing. The communication requirements between subsystems with coupling in the</br>cost function are that each subsystem obtain the previous optimal control trajectory of</br>those subsystems at each receding horizon update. The key requirements for stability</br>are that each distributed optimal control not deviate too far from the previous optimal</br>control, and that the receding horizon updates happen sufficiently fast. The theory is</br>applied in simulation for stabilization of a formation of vehicles. stabilization of a formation of vehicles.  +
• We consider the estimation of a vector sta … We consider the estimation of a vector state based on m measurements that can be potentially manipulated by an adversary. The attacker is assumed to have limited resources and can only manipulate up to l of the m measurements. However, it can the compromise measurements arbitrarily. The problem is formulated as a minimax optimization, where one seeks to construct an optimal estimator that minimizes the âworst-caseâ error against all possible manipulations by the attacker and all possible sensor noises. We show that if the system is not observable after removing 2l sensors, then the worst-case error is infinite, regardless of the estimation strategy. If the system remains observable after removing arbitrary set of 2l sensor, we prove that the optimal state estimation can be computed by solving a semidefinite programming problem. A numerical example is provided to illustrate the effectiveness of the proposed state estimator.ctiveness of the proposed state estimator.  +