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234
Consensus Seeking in Multiagent Systems under Dynamically Changing Interaction Topologies
, 2003
"... This note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. The note shows that i ..."
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Cited by 449 (37 self)
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This note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies. Both discrete and continuous update schemes are proposed for information consensus. The note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs across some time intervals has a spanning tree frequently enough as the system evolves. Simulation results show the effectiveness of our update schemes.
Basic problems in stability and design of switched systems
 IEEE Control Systems Magazine
, 1999
"... By a switched system, we mean a hybrid dynamical system consisting of a family of continuoustime subsystems and a rule that orchestrates the switching between them. This article surveys recent developments in three basic problems regarding stability and design of switched systems. These problems ar ..."
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Cited by 379 (10 self)
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By a switched system, we mean a hybrid dynamical system consisting of a family of continuoustime subsystems and a rule that orchestrates the switching between them. This article surveys recent developments in three basic problems regarding stability and design of switched systems. These problems are: stability for arbitrary switching sequences, stability for certain useful classes of switching sequences, and construction of stabilizing switching sequences. We also provide motivation for studying these problems by discussing how they arise in connection with various questions of interest in control theory and applications.
Quantized Feedback Stabilization of Linear Systems
 IEEE Trans. Automat. Control
, 2000
"... This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that ..."
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Cited by 293 (27 self)
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This paper addresses feedback stabilization problems for linear timeinvariant control systems with saturating quantized measurements. We propose a new control design methodology, which relies on the possibility of changing the sensitivity of the quantizer while the system evolves. The equation that describes the evolution of the sensitivity with time (discrete rather than continuous in most cases) is interconnected with the given system (either continuous or discrete), resulting in a hybrid system. When applied to systems that are stabilizable by linear timeinvariant feedback, this approach yields global asymptotic stability. Index TermsFeedback stabilization, hybrid system, linear control system, quantized measurement. I. INTRODUCTION T HIS PAPER deals with quantized feedback stabilization problems for linear timeinvariant control systems. A quantizer, as defined here, acts as a functional that maps a realvalued function into a piecewise constant function taking on a finite...
Stability of switched systems with average dwelltime
 In Proc. 38th IEEE Conf. on Decision and Control
, 1999
"... It is shown that switching among stable linear systems results in a stable system provided that switching is “slowontheaverage. ” In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, a ..."
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Cited by 219 (26 self)
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It is shown that switching among stable linear systems results in a stable system provided that switching is “slowontheaverage. ” In particular, it is proved that exponential stability is achieved when the number of switches in any finite interval grows linearly with the length of the interval, and the growth rate is sufficiently small. Moreover, the exponential stability is uniform over all switchings with the above property. For switched systems with inputs this guarantees that several inputtostate induced norms are bounded uniformly over all slowontheaverage switchings. These results extend to classes of nonlinear switched systems that satisfy suitable uniformity assumptions. In this paper it is also shown that, in a supervisory control context, scaleindependent hysteresis can produce switching that is slowontheaverage and therefore the results mentioned above can be used to study the stability of hysteresisbased adaptive control systems. 1
Stability criteria for switched and hybrid systems
 SIAM Review
, 2007
"... The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, an ..."
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Cited by 114 (8 self)
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The study of the stability properties of switched and hybrid systems gives rise to a number of interesting and challenging mathematical problems. The objective of this paper is to outline some of these problems, to review progress made in solving these problems in a number of diverse communities, and to review some problems that remain open. An important contribution of our work is to bring together material from several areas of research and to present results in a unified manner. We begin our review by relating the stability problem for switched linear systems and a class of linear differential inclusions. Closely related to the concept of stability are the notions of exponential growth rates and converse Lyapunov theorems, both of which are discussed in detail. In particular, results on common quadratic Lyapunov functions and piecewise linear Lyapunov functions are presented, as they represent constructive methods for proving stability, and also represent problems in which significant progress has been made. We also comment on the inherent difficulty of determining stability of switched systems in general which is exemplified by NPhardness and undecidability results. We then proceed by considering the stability of switched systems in which there are constraints on the switching rules, through both dwell time requirements and state dependent switching laws. Also in this case the theory of Lyapunov functions and the existence of converse theorems is reviewed. We briefly comment on the classical Lur’e problem and on the theory of stability radii, both of which contain many of the features of switched systems and are rich sources of practical results on the topic. Finally we present a list of questions and open problems which provide motivation for continued research in this area.
Control Using LogicBased Switching
 Trends in Control: A European Perspective
, 1998
"... this paper is to give a brief tutorial review of four different classes of hybrid systems of this type  each consists of a continuoustime process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic. Three of the logics, called prerouted switching, ..."
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Cited by 84 (19 self)
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this paper is to give a brief tutorial review of four different classes of hybrid systems of this type  each consists of a continuoustime process to be controlled, a parameterized family of candidate controllers, and an event driven switching logic. Three of the logics, called prerouted switching, hysteresis switching and dwelltime switching respectively, are simple strategies capable of determining in real time which candidate controller should be put in feedback with a process in order to achieve desired closedloop performance. The fourth, called cyclic switching, has been devised to solve the longstanding stabilizability problem which arises in the synthesis of identifierbased adaptive controllers because of the existence of points in parameter space where the estimated model upon which certainty equivalence synthesis is based, loses stabilizability
Design of Observers for Hybrid Systems
 In Hybrid Systems: Computation and Control, volume 2289 of LNCS
, 2002
"... A methodology for the design of dynamical observers for hybrid plants is proposed. The hybrid observer consists of two parts: a location observer and a continuous observer. The former identifies the current location of the hybrid plant, while the latter produces an estimate of the evolution of t ..."
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Cited by 77 (8 self)
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A methodology for the design of dynamical observers for hybrid plants is proposed. The hybrid observer consists of two parts: a location observer and a continuous observer. The former identifies the current location of the hybrid plant, while the latter produces an estimate of the evolution of the continuous state of the hybrid plant. A synthesis procedure is offered when a set of properties on the hybrid plant is satisfied.
Certainty equivalence implies detectability
, 1998
"... It is shown that any stabilizing, certainty equivalence control used within an adaptive control system, causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimator’s output error ep, for every frozen value of the index or paramet ..."
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Cited by 55 (27 self)
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It is shown that any stabilizing, certainty equivalence control used within an adaptive control system, causes the familiar interconnection of a controlled process and associated output estimator to be detectable through the estimator’s output error ep, for every frozen value of the index or parameter vector p upon which both the estimator and controller dynamics depend. The fact that certainty equivalence implies detectability has been known for some time – this has been shown to be so whenever the process model is linear and the controller and estimator models are also linear for every frozen value of p. In this paper, use is made of recently introduced concepts of inputtostate stability and detectability for nonlinear systems to prove that the same implication is valid in a more general, nonlinear setting.
Trajectorytracking and pathfollowing of underactuated autonomous vehicles with parametric modeling uncertainty
 IEEE TRANS. ON AUTOMAT. CONTR
, 2005
"... We address the problem of position trajectorytracking and pathfollowing control design for underactuated autonomous vehicles in the presence of possibly large modeling parametric uncertainty. For a general class of vehicles moving in either two or threedimensional space, we demonstrate how adaptiv ..."
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Cited by 46 (6 self)
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We address the problem of position trajectorytracking and pathfollowing control design for underactuated autonomous vehicles in the presence of possibly large modeling parametric uncertainty. For a general class of vehicles moving in either two or threedimensional space, we demonstrate how adaptive switching supervisory control can be combined with a nonlinear Lyapunovbased tracking control law to solve the problem of global boundedness and convergence of the position tracking error to a neighborhood of the origin that can be made arbitrarily small. The desired trajectory does not need to be of a particular type (e.g., trimming trajectories) and can be any sufficiently smooth bounded curve parameterized by time. We also show how these results can be applied to solve the pathfollowing problem, in which the vehicle is required to converge to and follow a path, without a specific temporal specification. We illustrate our design procedures through two vehicle control applications: a hovercraft (moving on a planar surface) and an underwater vehicle (moving in threedimensional space). Simulations results are presented and discussed.