Showing papers in "IEEE Transactions on Automatic Control in 2003"
TL;DR: A theoretical explanation for the observed behavior of the Vicsek model, which proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
Abstract: In a recent Physical Review Letters article, Vicsek et al. propose a simple but compelling discrete-time model of n autonomous agents (i.e., points or particles) all moving in the plane with the same speed but with different headings. Each agent's heading is updated using a local rule based on the average of its own heading plus the headings of its "neighbors." In their paper, Vicsek et al. provide simulation results which demonstrate that the nearest neighbor rule they are studying can cause all agents to eventually move in the same direction despite the absence of centralized coordination and despite the fact that each agent's set of nearest neighbors change with time as the system evolves. This paper provides a theoretical explanation for this observed behavior. In addition, convergence results are derived for several other similarly inspired models. The Vicsek model proves to be a graphic example of a switched linear system which is stable, but for which there does not exist a common quadratic Lyapunov function.
8,233 citations
TL;DR: It is shown that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time and an explicit bound on the swarm size is obtained, which depends only on the parameters of the swarm model.
Abstract: In this note, we specify an "individual-based" continuous-time model for swarm aggregation in n-dimensional space and study its stability properties. We show that the individuals (autonomous agents or biological creatures) will form a cohesive swarm in a finite time. Moreover, we obtain an explicit bound on the swarm size, which depends only on the parameters of the swarm model.
929 citations
TL;DR: The design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators are presented.
Abstract: Planar, underactuated, biped walkers form an important domain of applications for hybrid dynamical systems. This paper presents the design of exponentially stable walking controllers for general planar bipedal systems that have one degree-of-freedom greater than the number of available actuators. The within-step control action creates an attracting invariant set - a two-dimensional zero dynamics submanifold of the full hybrid model $whose restriction dynamics admits a scalar linear time-invariant return map. Exponentially stable periodic orbits of the zero dynamics correspond to exponentially stabilizable orbits of the full model. A convenient parameterization of the hybrid zero dynamics is imposed through the choice of a class of output functions. Parameter optimization is used to tune the hybrid zero dynamics in order to achieve closed-loop, exponentially stable walking with low energy consumption, while meeting natural kinematic and dynamic constraints. The general theory developed in the paper is illustrated on a five link walker, consisting of a torso and two legs with knees.
863 citations
TL;DR: Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata and a class of hybrids whose solutions depend continuously on the initial state is characterized.
Abstract: Hybrid automata provide a language for modeling and analyzing digital and analogue computations in real-time systems. Hybrid automata are studied here from a dynamical systems perspective. Necessary and sufficient conditions for existence and uniqueness of solutions are derived and a class of hybrid automata whose solutions depend continuously on the initial state is characterized. The results on existence, uniqueness, and continuity serve as a starting point for stability analysis. Lyapunov's theorem on stability via linearization and LaSalle's invariance principle are generalized to hybrid automata.
850 citations
TL;DR: A state space framework for posing problems of this type, and focus on systems whose model is spatially discrete, is developed using the l/sub 2/-induced norm as the performance criterion.
Abstract: This paper deals with analysis, synthesis, and implementation of distributed controllers, designed for spatially interconnected systems. We develop a state space framework for posing problems of this type, and focus on systems whose model is spatially discrete. In this paper, analysis and synthesis results are developed for this class of systems using the l/sub 2/-induced norm as the performance criterion. The results are stated in terms of linear matrix inequalities and are thus readily amenable to computation. A special implementation of the resulting controllers is presented, which is particularly attractive for distributed operation of the controller. Several examples are provided to further illustrate the application of the results.
838 citations
TL;DR: This work proposes a general theory for constrained moving horizon estimation, and applies this theory to develop a practical algorithm for constrained linear and nonlinear state estimation.
Abstract: State estimator design for a nonlinear discrete-time system is a challenging problem, further complicated when additional physical insight is available in the form of inequality constraints on the state variables and disturbances. One strategy for constrained state estimation is to employ online optimization using a moving horizon approximation. We propose a general theory for constrained moving horizon estimation. Sufficient conditions for asymptotic and bounded stability are established. We apply these results to develop a practical algorithm for constrained linear and nonlinear state estimation. Examples are used to illustrate the benefits of constrained state estimation. Our framework is deterministic.
771 citations
TL;DR: In this paper, the notion of monotonicity is extended to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components.
Abstract: Monotone systems constitute one of the most important classes of dynamical systems used in mathematical biology modeling. The objective of this paper is to extend the notion of monotonicity to systems with inputs and outputs, a necessary first step in trying to understand interconnections, especially including feedback loops, built up out of monotone components. Basic definitions and theorems are provided, as well as an application to the study of a model of one of the cell's most important subsystems.
694 citations
TL;DR: It is shown that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective, and the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws.
Abstract: A new method to design asymptotically stabilizing and adaptive control laws for nonlinear systems is presented. The method relies upon the notions of system immersion and manifold invariance and, in principle, does not require the knowledge of a (control) Lyapunov function. The construction of the stabilizing control laws resembles the procedure used in nonlinear regulator theory to derive the (invariant) output zeroing manifold and its friend. The method is well suited in situations where we know a stabilizing controller of a nominal reduced order model, which we would like to robustify with respect to higher order dynamics. This is achieved by designing a control law that asymptotically immerses the full system dynamics into the reduced order one. We also show that in adaptive control problems the method yields stabilizing schemes that counter the effect of the uncertain parameters adopting a robustness perspective. Our construction does not invoke certainty equivalence, nor requires a linear parameterization, furthermore, viewed from a Lyapunov perspective, it provides a procedure to add cross terms between the parameter estimates and the plant states. Finally, it is shown that the proposed approach is directly applicable to systems in feedback and feedforward form, yielding new stabilizing control laws. We illustrate the method with several academic and practical examples, including a mechanical system with flexibility modes, an electromechanical system with parasitic actuator dynamics and an adaptive nonlinearly parameterized visual servoing application.
683 citations
TL;DR: In this paper, the authors considered the problem of robust H/sup /spl infin/ filtering for uncertain Markovian jump linear systems with time-delays which are time-varying and depend on the system mode.
Abstract: This paper considers the problem of robust H/sup /spl infin// filtering for uncertain Markovian jump linear systems with time-delays which are time-varying and depend on the system mode. The parameter uncertainties are time-varying norm-bounded. The aim of this problem is to design a Markovian jump linear filter that ensures robust exponential mean-square stability of the filtering error system and a prescribed L/sub 2/- induced gain from the noise signals to the estimation error, for all admissible uncertainties. A sufficient condition for the solvability of this problem is obtained. The desired filter can be constructed by solving a set of linear matrix inequalities. An illustrative numerical example is provided to demonstrate the effectiveness of the proposed approach.
536 citations
TL;DR: It is shown that, if (and only if) the plant is asymptotically stable, plant-order linear antiwind up compensation is always feasible for large enough L/sub 2/ gain and that static antiwindup compensation is feasible provided a quasi-common Lyapunov function, between the open-loop and unconstrained closed-loop, exists.
Abstract: This paper considers closed-loop quadratic stability and L/sub 2/ performance properties of linear control systems subject to input saturation. More specifically, these properties are examined within the context of the popular linear antiwindup augmentation paradigm. Linear antiwindup augmentation refers to designing a linear filter to augment a linear control system subject to a local specification, called the "unconstrained closed-loop behavior." Building on known results on H/sub /spl infin// and LPV synthesis, the fixed order linear antiwindup synthesis feasibility problem is cast as a nonconvex matrix optimization problem, which has an attractive system theoretic interpretation: the lower bound on the achievable L/sub 2/ performance is the maximum of the open and unconstrained closed-loop L/sub 2/ gains. In the special cases of zero-order (static) and plant-order antiwindup compensation, the feasibility conditions become (convex) linear matrix inequalities. It is shown that, if (and only if) the plant is asymptotically stable, plant-order linear antiwindup compensation is always feasible for large enough L/sub 2/ gain and that static antiwindup compensation is feasible provided a quasi-common Lyapunov function, between the open-loop and unconstrained closed-loop, exists. Using the solutions to the matrix feasibility problems, the synthesis of the antiwindup augmentation achieving the desired level of L/sub 2/ performance is then accomplished by solving an additional LMI.
529 citations
TL;DR: It is shown that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs.
Abstract: For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.
TL;DR: The proposed composite nonlinear feedback control technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations and can be applied to design servo systems that deal with "point-and-shoot" fast targeting.
Abstract: We study in this paper the theory and applications of a nonlinear control technique, i.e., the so-called composite nonlinear feedback control, for a class of linear systems with actuator nonlinearities. It consists of a linear feedback law and a nonlinear feedback law without any switching element. The linear feedback part is designed to yield a closed-loop system with a small damping ratio for a quick response, while at the same time not exceeding the actuator limits for the desired command input levels. The nonlinear feedback law is used to increase the damping ratio of the closed-loop system as the system output approaches the target reference to reduce the overshoot caused by the linear part. It is shown that the proposed technique is capable of beating the well-known time-optimal control in the asymptotic tracking situations. The application of such a new technique to an actual hard disk drive servo system shows that it outperforms the conventional method by more than 30%. The technique can be applied to design servo systems that deal with "point-and-shoot" fast targeting.
TL;DR: It is proved that the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed-loop system signals and disturbance attenuation.
Abstract: Presents a robust adaptive control approach for a class of time-varying uncertain nonlinear systems in the strict feedback form with completely unknown time-varying virtual control coefficients, uncertain time-varying parameters and unknown time-varying bounded disturbances. The proposed design method does not require any a priori knowledge of the unknown coefficients except for their bounds. It is proved that the proposed robust adaptive scheme can guarantee the global uniform ultimate boundedness of the closed-loop system signals and disturbance attenuation.
TL;DR: It is shown that the flow-pipe approximation error can be made arbitrarily small for general nonlinear dynamics and that the computations can bemade more efficient for affine systems.
Abstract: This paper concerns computational methods for verifying properties of polyhedral invariant hybrid automata (PIHA), which are hybrid automata with discrete transitions governed by polyhedral guards. To verify properties of the state trajectories for PIHA, the planar switching surfaces are partitioned to define a finite set of discrete states in an approximate quotient transition system (AQTS). State transitions in the AQTS are determined by the reachable states, or flow pipes, emitting from the switching surfaces according to the continuous dynamics. This paper presents a method for computing polyhedral approximations to flow pipes. It is shown that the flow-pipe approximation error can be made arbitrarily small for general nonlinear dynamics and that the computations can be made more efficient for affine systems. The paper also describes CheckMate, a MATLAB-based tool for modeling, simulating and verifying properties of hybrid systems based on the computational methods previously described.
TL;DR: This note introduces a distributed delay control law that assigns a finite closed-loop spectrum and whose implementation with a sum of point-wise delays is safe, and which leads to a closed- loop characteristic quasipolynomial of retarded type.
Abstract: The instability mechanisms, related to the implementation of distributed delay controllers in the context of finite spectrum assignment, were studied in detail in the past few years. In this note we introduce a distributed delay control law that assigns a finite closed-loop spectrum and whose implementation with a sum of point-wise delays is safe. This property is obtained by implicitly including a low-pass filter in the control loop. This leads to a closed-loop characteristic quasipolynomial of retarded type, and not one of neutral type, which was shown to be a cause of instability in previous schemes.
TL;DR: A state-based approach for online passive fault diagnosis in systems modeled as finite-state automata is presented, and necessary and sufficient conditions for failure diagnosability are derived.
Abstract: A state-based approach for online passive fault diagnosis in systems modeled as finite-state automata is presented. In this framework, the system and the diagnoser (the fault detection system) do not have to be initialized at the same time. Furthermore, no information about the state or even the condition (failure status) of the system before the initiation of diagnosis is required. The design of the fault detection system, in the worst case, has exponential complexity. A model reduction scheme with polynomial time complexity is introduced to reduce the computational complexity of the design. Diagnosability of failures is studied, and necessary and sufficient conditions for failure diagnosability are derived.
TL;DR: The addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities.
Abstract: In this note, we consider a new filtering problem for linear uncertain discrete-time stochastic systems with missing measurements. The parameter uncertainties are allowed to be norm-bounded and enter into the state matrix. The system measurements may be unavailable (i.e., missing data) at any sample time, and the probability of the occurrence of missing data is assumed to be known. The purpose of this problem is to design a linear filter such that, for all admissible parameter uncertainties and all possible incomplete observations, the error state of the filtering process is mean square bounded, and the steady-state variance of the estimation error of each state is not more than the individual prescribed upper bound. It is shown that, the addressed filtering problem can effectively be solved in terms of the solutions of a couple of algebraic Riccati-like inequalities or linear matrix inequalities. The explicit expression of the desired robust filters is parameterized, and an illustrative numerical example is provided to demonstrate the usefulness and flexibility of the proposed design approach.
TL;DR: A relationship between the number of values taken by the encoder and the norm of the transition matrix of the open-loop system over one sampling period is derived, which guarantees that global asymptotic stabilization can be achieved.
Abstract: We consider the problem of stabilizing a linear time-invariant system using sampled encoded measurements of its state or output. We derive a relationship between the number of values taken by the encoder and the norm of the transition matrix of the open-loop system over one sampling period, which guarantees that global asymptotic stabilization can be achieved. A coding scheme and a stabilizing control strategy are described explicitly.
TL;DR: It is proved that the proposed systematic backstepping design method is able to guarantee semiglobally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.
Abstract: In this note, adaptive neural control is presented for a class of strict-feedback nonlinear systems with unknown time delays. Using appropriate Lyapunov-Krasovskii functionals, the uncertainties of unknown time delays are compensated for such that iterative backstepping design can be carried out. In addition, controller singularity problems are solved by using the integral Lyapunov function and employing practical robust neural network control. The feasibility of neural network approximation of unknown system functions is guaranteed over practical compact sets. It is proved that the proposed systematic backstepping design method is able to guarantee semiglobally uniformly ultimate boundedness of all the signals in the closed-loop system and the tracking error is proven to converge to a small neighborhood of the origin.
TL;DR: This paper introduces a simpler design, termed a jump linear estimator (JLE), to cope with losses, and introduces a special class of JLE, termed finite loss history estimators (FLHE), which uses a canonical gain selection logic.
Abstract: In this paper, we consider estimation with lossy measurements. This problem can arise when measurements are communicated over wireless channels. We model the plant/measurement loss process as a Markovian jump linear system. While the time-varying Kalman estimator (TVKE) is known to be optimal, we introduce a simpler design, termed a jump linear estimator (JLE), to cope with losses. A JLE has predictor/corrector form, but at each time selects a corrector gain from a finite set of precalculated gains. The motivation for the JLE is twofold. The computational burden of the JLE is less than that of the TVKE and the estimation errors expected when using JLE provide an upper bound for those expected when using TVKE. We then introduce a special class of JLE, termed finite loss history estimators (FLHE), which uses a canonical gain selection logic. A notion of optimality for the FLHE is defined and an optimal synthesis method is given. The proposed design method is compared to TVKE in a simulation study.
TL;DR: In this paper, delay-dependent robust full-order and reduced-order filters for a class of nonlinear systems with multiple time-varying delays in the state and parameter uncertainties residing in a polytope are presented.
Abstract: This note presents delay-dependent robust H/sub /spl infin// and L/sub 2/-L/sub /spl infin// filter designs for a class of nonlinear systems with multiple time-varying delays in the state and parameter uncertainties residing in a polytope. The nonlinearities are assumed to satisfy global Lipschitz conditions. Attention is focused on the design of robust full-order and reduced-order filters guaranteeing a prescribed noise attenuation level in an H/sub /spl infin// or L/sub 2/-L/sub /spl infin// sense. The admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms.
TL;DR: It is shown that, for a system under a given saturated linear feedback, the convex hull of a set of invariant ellipsoids is also invariant, which is used to study the set invariance properties of continuous-time linear systems with input and state constraints.
Abstract: A Lyapunov function based on a set of quadratic functions is introduced in this paper. We call this Lyapunov function a composite quadratic function. Some important properties of this Lyapunov function are revealed. We show that this function is continuously differentiable and its level set is the convex hull of a set of ellipsoids. These results are used to study the set invariance properties of continuous-time linear systems with input and state constraints. We show that, for a system under a given saturated linear feedback, the convex hull of a set of invariant ellipsoids is also invariant. If each ellipsoid in a set can be made invariant with a bounded control of the saturating actuators, then their convex hull can also be made invariant by the same actuators. For a set of ellipsoids, each invariant under a separate saturated linear feedback, we also present a method for constructing a nonlinear continuous feedback law which makes their convex hull invariant.
TL;DR: A so-called true concurrency approach, in which no global state and no global time is available, is followed, which uses only local states in combination with a partial order model of time.
Abstract: In this paper, we consider the diagnosis of asynchronous discrete event systems. We follow a so-called true concurrency approach, in which no global state and no global time is available. Instead, we use only local states in combination with a partial order model of time. Our basic mathematical tool is that of net unfoldings originating from the Petri net research area. This study was motivated by the problem of event correlation in telecommunications network management.
TL;DR: The global asymptotic stabilization by output feedback for systems whose dynamics are in a feedback form and where the nonlinear terms admit an incremental rate depending only on the measured output is studied.
Abstract: We study the global asymptotic stabilization by output feedback for systems whose dynamics are in a feedback form and where the nonlinear terms admit an incremental rate depending only on the measured output. The output feedback we consider is of the observer-controller type where the design of the controller follows from standard robust backstepping. The novelty is in the observer which is high-gain such as with a gain coming from a Riccati equation.
TL;DR: A delay-independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities, based on which the corresponding reaching motion controller is developed.
Abstract: This note is devoted to robust sliding-mode control for time-delay systems with mismatched parametric uncertainties. A delay-independent sufficient condition for the existence of linear sliding surfaces is given in terms of linear matrix inequalities, based on which the corresponding reaching motion controller is also developed. The results are illustrated by an example.
TL;DR: A new iterative state-feedback controller design procedure is proposed, based on a new bounded real lemma derived upon an inequality recently proposed by Moon (2001), which solves both the instantaneous and delayed feedback problems in a unified framework.
Abstract: This paper presents some comments and further results concerning the descriptor system approach to H/sub /spl infin// control of linear time-delay systems. Upon the system model of the paper by Fridman and Shaked (2001), we propose a new iterative state-feedback controller design procedure, which is based on a new bounded real lemma derived upon an inequality recently proposed by Moon (2001). The proposed design solves both the instantaneous and delayed feedback problems in a unified framework, and is illustrated by a numerical example to be much less conservative than the above paper and other relevant references.
TL;DR: A new algorithm for estimating constant biases in gyro measurements of angular velocity is proposed, and it is demonstrated that the resulting estimates converge to the true bias values exponentially fast.
Abstract: We propose a new algorithm for estimating constant biases in gyro measurements of angular velocity, and demonstrate that the resulting estimates converge to the true bias values exponentially fast. The new observer is then combined with a nonlinear attitude tracking control strategy in a certainty equivalence fashion, and the combination shown via Lyapunov analysis to produce globally stable closed-loop dynamics, with asymptotically perfect tracking of any commanded attitude sequence. The analysis is then extended to consider the effects of stochastic measurement noise in the gyro in addition to the bias. A simulation is given for a rigid spacecraft tracking a specified, time-varying attitude sequence to illustrate the theoretical claims.
TL;DR: In this article, a model of an M-dimensional asynchronous mobile swarm with a fixed communication topology, where each member only communicates with fixed neighbors, is studied and conditions under which collision-free convergence can be achieved with finite-size swarm members that have proximity sensors, and neighbor position sensors that only provide delayed position information.
Abstract: Coordinated dynamical swarm behavior occurs when certain types of animals forage for food or try to avoid predators. Analogous behaviors can occur in engineering systems (e.g., in groups of autonomous mobile robots or air vehicles). In this paper, we study a model of an M-dimensional (M/spl ges/2) asynchronous swarm with a fixed communication topology, where each member only communicate with fixed neighbors, to provide conditions under which collision-free convergence can be achieved with finite-size swarm members that have proximity sensors, and neighbor position sensors that only provide delayed position information. Moreover, we give conditions under which an M-dimensional asynchronous mobile swarm with a fixed communication topology following an "edge-leader" can maintain cohesion during movements even in the presence of sensing delays and asynchronism. In addition, the swarm movement flexibility is analyzed. Such stability analysis is of fundamental importance if one wants to understand the coordination mechanisms for groups of autonomous vehicles or robots, where intermember communication channels are less than perfect and collisions must be avoided.
TL;DR: A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory.
Abstract: This paper gives a unified approach to feedback control theory of quantum mechanical systems of bosonic modes described by noncommutative operators. A quantum optical closed-loop, including a plant and controller, is developed and its fundamental structural properties are analyzed extensively from a purely quantum mechanical point of view, in order to facilitate the use of control theory in microscopic world described by quantum theory. In particular, an input-output description of quantum mechanical systems which is essential in describing the behavior of the feedback systems is fully formulated and developed. This would then provide a powerful tool for quantum control and pave an avenue that connects control theory to quantum dynamics. This paper is divided into two parts. The first part is devoted to the basic formulation of quantum feedback control via quantum communication and local operations on an optical device, cavity, that can be regarded as a unit of quantum dynamics of bosonic modes. The formulation introduced in this paper presents the feature intrinsic in quantum feedback systems based on quantum stochastic differential equations. The input-output description provides a basis for developing quantum feedback control through the transfer function representation of quantum feedback systems. In the follow-up paper, the quantum mechanical representation of feedback is further elaborated to yield the control theoretical representation of fundamental notions of quantum theory, uncertainty principle, e.g., and some applications are presented.