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Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
, 2002
"... In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent headings. Each agent's heading is updated using a local rule based on the a ..."
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Cited by 604 (44 self)
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In a recent Physical Review Letters paper, Vicsek et. al. propose a simple but compelling discretetime model of n autonomous agents fi.e., points or particlesg all moving in the plane with the same speed but with dierent 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.
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 67 (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
A necessary and sufficient condition for consensus over random networks
 IEEE Transactions on Automatic Control
, 2008
"... Abstract — In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discretetime and continuoustime stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discre ..."
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Cited by 20 (2 self)
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Abstract — In this paper we consider the consensus problem for stochastic switched linear dynamical systems. For discretetime and continuoustime stochastic switched linear systems, we present necessary and sufficient conditions under which such systems reach a consensus almost surely. In the discretetime case, our assumption is that the underlying graph of the system at any given time instance is derived from a random graph process, independent of other time instances. These graphs can be weighted, directed and with dependent edges. For the continuoustime case, we assume that the switching is governed by a Poisson point process and the graphs characterizing the topology of the system are independent and identically distributed over time. For both such frameworks, we present necessary and sufficient conditions for almost sure asymptotic consensus using simple ergodicity and probabilistic arguments. These easily verifiable conditions depend on the spectrum of the average weight matrix and the average Laplacian matrix for the discretetime and continuoustime cases, respectively. I.
Asymptotic Properties of Nonlinear Feedback Control Systems
, 1998
"... Asymptotic Properties of Nonlinear Feedback Control Systems A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts by Daniel Liberzon We study asymptotic behaviour of nonlinear feedback control systems, both deterministic an ..."
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Cited by 8 (6 self)
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Asymptotic Properties of Nonlinear Feedback Control Systems A dissertation presented to the Faculty of the Graduate School of Arts and Sciences of Brandeis University, Waltham, Massachusetts by Daniel Liberzon We study asymptotic behaviour of nonlinear feedback control systems, both deterministic and stochastic. Of particular interest is the case of quantized feedback, i.e., when the nonlinearity takes the form of a specific piecewise constant function. In the context of deterministic linear control systems with quantized measurements, we show how quantized feedback can be used to asymptotically stabilize the system (Chapter II). For systems perturbed by white noise, we address the question of existence of steadystate probability distributions. In the linear case, the solution to the v FokkerPlanck equation which describes the evolution of the probability density is well known. In particular, one has an expression for the steadystate probability density, which is an eigenfunction...
Coordination of Distributed Autonomous Systems
, 2004
"... This thesis focuses on the analysis of emergent behaviors of a multiagent system. The ultimate aim is to synthesize complex group behaviors from simple social interactions among individuals based on simple strategies. One of the many challenges in the study of emergent behaviors of multiagent sys ..."
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Cited by 1 (0 self)
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This thesis focuses on the analysis of emergent behaviors of a multiagent system. The ultimate aim is to synthesize complex group behaviors from simple social interactions among individuals based on simple strategies. One of the many challenges in the study of emergent behaviors of multiagent systems is characterizing the local properties of each agent that will lead to global emergent behaviors. Two types of emergent behaviors are described, namely, the Multiagent Flocking Problem and the Multiagent Rendezvous Problem. In both problems, provably correct distributed local rules are proposed. In the Flocking problem, a local heading average rule was studied and convergence of the group heading to a common unspecified heading was proved using results in convergence of matrix products in Markov Chains. Replacing the word agent by a more general notion of identity naturally leads the Flocking problem to a class of network consensus problems. In the Rendezvous problem, convergence of the group positions to a common unspecified location was established using combinations of convex analysis and standard Lyapunov function approach. An asynchronous version of the Rendezvous problem was also solved by modelling the process using a suitably defined hybrid model and a procedure called Analytic Synchronization. Recent applications of the Controlled Mobility concept to wireless network in both synchronous and asynchronous settings to optimize energy consumption is briefly discussed at the end.