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35
Flocking in Fixed and Switching Networks
, 2003
"... The work of this paper is inspired by the flocking phenomenon observed in Reynolds (1987). We introduce a class of local control laws for a group of mobile agents that result in: (i) global alignment of their velocity vectors, (ii) convergence of their speeds to a common one, (iii) collision avoidan ..."
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Cited by 192 (10 self)
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The work of this paper is inspired by the flocking phenomenon observed in Reynolds (1987). We introduce a class of local control laws for a group of mobile agents that result in: (i) global alignment of their velocity vectors, (ii) convergence of their speeds to a common one, (iii) collision avoidance, and (iv) minimization of the agents artificial potential energy. These are made possible through local control action by exploiting the algebraic graph theoretic properties of the underlying interconnection graph. Algebraic connectivity a#ects the performance and robustness properties of the overall closed loop system. We show how the stability of the flocking motion of the group is directly associated with the connectivity properties of the interconnection network and is robust to arbitrary switching of the network topology.
Gossip coverage control for robotic networks: Dynamical systems on the the space of partitions
, 2009
"... Abstract. Future applications in environmental monitoring, delivery of services and transportation of goods motivate the study of deployment and partitioning tasks for groups of autonomous mobile agents. These tasks may be achieved by recent coverage algorithms, based upon the classic methods by Llo ..."
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Cited by 18 (11 self)
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Abstract. Future applications in environmental monitoring, delivery of services and transportation of goods motivate the study of deployment and partitioning tasks for groups of autonomous mobile agents. These tasks may be achieved by recent coverage algorithms, based upon the classic methods by Lloyd. These algorithms however rely upon critical requirements on the communication network: information is exchanged synchronously among all agents and longrange communication is sometimes required. This work proposes novel coverage algorithms that require only gossip communication, i.e., asynchronous, pairwise, and possibly unreliable communication. Which robot pair communicates at any given time may be selected deterministically or randomly. A key innovative idea is describing coverage algorithms for robot deployment and environment partitioning as dynamical systems on a space of partitions. In other words, we study the evolution of the regions assigned to each agent rather than the evolution of the agents ’ positions. The proposed gossip algorithms are shown to converge to centroidal Voronoi partitions under mild technical conditions. Our treatment features a broad variety of results in topology, analysis and geometry. First, we establish the compactness of a suitable space of partitions with respect to the symmetric difference metric. Second, with respect to this metric, we establish the continuity of various geometric maps, including the Voronoi diagram as a function of its generators, the location of a centroid as a function of a set, and the widelyknown multicenter function studied in facility location problems. Third, we prove two convergence theorems for dynamical systems on metric spaces described by deterministic and stochastic switches. Key words. Cooperative control, multiagent systems, gossip communication, geometric optimization, centroidal Voronoi tessellations, Lloyd algorithm AMS subject classifications. 37N35, 68T40, 68W15, 93D20, 03H05
Lyapunov stability of complementarity and extended systems
 SIAM J. Optim
"... Abstract. A linear complementarity system (LCS) is a piecewise linear dynamical system consisting of a linear timeinvariant ordinary differential equation (ODE) parameterized by an algebraic variable that is required to be a solution to a finitedimensional linear complementarity problem (LCP), wh ..."
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Cited by 15 (4 self)
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Abstract. A linear complementarity system (LCS) is a piecewise linear dynamical system consisting of a linear timeinvariant ordinary differential equation (ODE) parameterized by an algebraic variable that is required to be a solution to a finitedimensional linear complementarity problem (LCP), whose constant vector is a linear function of the differential variable. Continuing the authors’ recent investigation of the LCS from the combined point of view of system theory and mathematical programming, this paper addresses the important systemtheoretic properties of exponential and asymptotic stability for an LCS with a C1 state trajectory. The novelty of our approach lies in our employment of a quadratic Lyapunov function that involves the auxiliary algebraic variable of the LCS; when expressed in the state variable alone, the Lyapunov function is piecewise quadratic, and thus nonsmooth. The nonsmoothness feature invalidates standard stability analysis that is based on smooth Lyapunov functions. In addition to providing sufficient conditions for exponential stability, we establish a generalization of the wellknown LaSalle invariance theorem for the asymptotic stability of a smooth dynamical system to the LCS, which is intrinsically a nonsmooth system. Sufficient matrixtheoretic copositivity conditions are introduced to facilitate the verification of the stability properties. Properly specialized, the latter conditions are satisfied by a passivelike LCS and certain hybrid linear systems having common quadratic Lyapunov functions. We provide numerical examples to illustrate the stability results. We also develop an extended local exponential stability theory for nonlinear complementarity systems and differential variational inequalities, based on a new converse theorem for ODEs with Bdifferentiable righthand sides. The latter theorem asserts that the existence of a “Bdifferentiable Lyapunov function ” is a necessary and sufficient condition for the exponential stability of an equilibrium of such a differential system.
Switching Stabilizability for ContinuousTime Uncertain Switched Linear Systems
, 2007
"... This paper investigates the switching stabilizability problem for a class of continuoustime switched linear systems with timevariant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived, under ..."
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Cited by 14 (2 self)
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This paper investigates the switching stabilizability problem for a class of continuoustime switched linear systems with timevariant parametric uncertainties. First, a necessary and sufficient condition for the asymptotic stabilizability of such uncertain switched linear system is derived, under the assumption that the closedloop switched system does not generate sliding motions. Then, an additional condition is introduced to exclude the possibility of unstable sliding motions. Finally, a necessary and sufficient for the asymptotic stabilizability of such continuoustime uncertain switched linear systems is presented. This result improves upon conditions found in the literature which are either sufficient only or necessary only.
LaSalleYoshizawa Corollaries for Nonsmooth Systems
, 2013
"... In this technical note, two generalized corollaries to the LaSalleYoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous righthand sides. Lyapunovbased analysis methods that achieve asymptotic convergence when the candidate Lyap ..."
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Cited by 10 (4 self)
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In this technical note, two generalized corollaries to the LaSalleYoshizawa Theorem are presented for nonautonomous systems described by nonlinear differential equations with discontinuous righthand sides. Lyapunovbased analysis methods that achieve asymptotic convergence when the candidate Lyapunov derivative is upper bounded by a negative semidefinite function in the presence of differential inclusions are presented. A design example illustrates the utility of the corollaries.
Synchonization in Oscillator Networks with Heterogeneous Delays, Switching Topologies and Nonlinear Dynamics
, 2006
"... This paper investigates the attractivity properties of the lockedinphase equilibria set in oscillator networks, in the presence of multiple, noncommensurate communication delays. The dynamics that the oscillators are endowed with are in the form of nonlinear delay differential equations, with Ku ..."
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Cited by 8 (0 self)
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This paper investigates the attractivity properties of the lockedinphase equilibria set in oscillator networks, in the presence of multiple, noncommensurate communication delays. The dynamics that the oscillators are endowed with are in the form of nonlinear delay differential equations, with Kuramototype interactions. Using an appropriate LaSalle invariance principle we assess the attractivity properties of this set for arbitrary topology interconnections. We then show that this set is also asymptotically attracting even if the network topology is allowed to change.
Input to state stability and allied system properties. Autom Remote Control 72:1579–1614
, 2011
"... AbstractThe main results obtained in the field of inputstate stable systems and systems with other similar characteristics that were published over the last two decades were reviewed. ..."
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Cited by 8 (7 self)
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AbstractThe main results obtained in the field of inputstate stable systems and systems with other similar characteristics that were published over the last two decades were reviewed.
Effects of Delay in MultiAgent Consensus and Oscillator Synchronization
"... The coordinated motion of multiagent systems and oscillator synchronization are two important examples of networked control systems. In this paper, we consider what effect multiple, noncommensurate (heterogeneous) communication delays can have on the consensus properties of largescale multiagent ..."
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Cited by 6 (0 self)
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The coordinated motion of multiagent systems and oscillator synchronization are two important examples of networked control systems. In this paper, we consider what effect multiple, noncommensurate (heterogeneous) communication delays can have on the consensus properties of largescale multiagent systems endowed with nonlinear dynamics. We show that the structure of the delayed dynamics allows functionality to be retained for arbitrary communication delays, even for switching topologies under certain connectivity conditions. The results are extended to the related problem of oscillator synchronization.
Chemical networks with inflows and outflows: A positive linear differential inclusions approach
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