On robust control algorithms for nonlinear network consensus protocols

Hui, Qing; Haddad, Wassim M.; Bhat, Sanjay P.

doi:10.1002/rnc.1426

Cited by 28 publications

(6 citation statements)

References 26 publications

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“…Communication over networks is often unreliable and noisy. This inspired research on the robustness of consensus algorithms [43,44,22,14,16,40]. In [27], robustness was discussed for average consensus algorithms.…”

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confidence: 99%

Robust Consensus for Continuous-Time Multiagent Dynamics

Shi¹,

Johansson²

2013

SIAM J. Control Optim.

131

106

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This paper investigates consensus problems for continuous-time multiagent systems with time-varying communication graphs subject to input noise. Based on input-to-state stability and integral input-to-state stability, robust consensus and integral robust consensus are defined with respect to L∞ and L 1 norms of the noise function, respectively. Sufficient and/or necessary connectivity conditions are obtained for the system to reach robust consensus or integral robust consensus under mild assumptions. The results answer the question on how much interaction is required for a multiagent network to converge despite a certain amount of input disturbance. The -convergence time is obtained for the consensus computation on directed and K-bidirectional graphs. Introduction.Coordination of multiagent networks has attracted a significant amount of attention in the past few years, due to its broad applications in various fields of science including physics, engineering, biology, ecology, and social science [42,15,25,21,9]. Distributed control using neighboring information flow has been shown to ensure collective tasks such as formation, flocking, rendezvous, and aggregation [24,17,18,19,30].Central to multiagent coordination is the study of consensus, or state agreement, which requires that all agents achieve a common state. The idea of distributed consensus arose as early as 1980s in the classical work [41] for the study of distributed optimization methods. Since then consensus seeking has been extensively studied in the literature for both continuous-time and discrete-time models [15,21,38,39,3,4,28,18,45,46,49,48], where node interactions are carried out over an underlying communication graph. The connectivity of this communication graph plays a key role in consensus analysis. The "joint connectivity," i.e., connectivity defined on the union graph over a time interval, and similar concepts are important in the analysis of consensus stability with time-dependent topology. Uniformly joint connectivity, which requests that the union graph be connected for all intervals longer than some positive constant, has been employed for consensus problems for discrete-time and continuous-time agent dynamics, as well as directed and undirected interconnection topologies [41,15,18,13,6]. In [15], the authors proved the consensus of a simplified Vicsek model under uniformly joint connectivity, followed by some more precise analysis in [3,4,28]. In [13] and [6], the jointly connected coordination was investigated for second-order agent dynamics. A nonlinear continuous-time *

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confidence: 99%

Robust Consensus for Continuous-Time Multiagent Dynamics

Shi¹,

Johansson²

2013

SIAM J. Control Optim.

131

106

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“…Indeed, it is possible for a trajectory to converge to the set of equilibria without converging to any one equilibrium point as examples in [32] show. Conversely, semistability does not imply that the equilibrium set is asymptotically stable in any accepted sense [33]. This is because stability of sets is defined in terms of distance (especially in case of noncompact sets), and it is possible to construct examples in which the dynamical system is semistable, but the domain of semistability contains no ε-neighborhood (defined in terms of the distance) of the (noncompact) equilibrium set, thus ruling out asymptotic stability of the equilibrium set.…”

Section: Definition 41: I) the Linear Time-varying Iterationmentioning

confidence: 99%

Lyapunov-based semistability analysis for discrete-time switched network systems

Hui

2011

Proceedings of the 2011 American Control Conference

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In this paper, we address semistability analysis of a class of distributed iterative algorithms for discretetime switched network systems. Semistability is the property whereby every solution that starts in a neighborhood of a Lyapunov stable equilibrium converges to a (possibly different) Lyapunov stable equilibrium. To this end, we use a Lyapunovbased approach to develop a series of sufficient conditions for semistability of discrete-time switched systems. This technique gives us a new perspective to design distributed numerical iterative algorithms for network systems from a dynamical systems viewpoint. Despite the fact that distributed iterative algorithms in general are not dynamical systems, the methods we used for proving convergence of dynamical systems are somehow valid for a large class of distributed iterative algorithms in network systems. The motivation of this paper exactly follows from this general observation. Part of the effort by this paper can be viewed as an attempt to analyze distributed numerical algorithms for network systems from a control perspective.

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“…Especially, the design of distributed control algorithms based on agent's local interaction information in multi-agent networks such as rendezvous control of multinonholonomic agents [8], formation control [2,15], and flocking attitude alignment [4,23], has drawn much attention from researchers due to its broad range of applications. The formation control, flocking, and rendezvous, can be unified in the general framework of consensus setting.…”

Section: Introductionmentioning

confidence: 99%

Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies

Li,

Liao,

Huang

et al. 2014

Information Sciences

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On robust control algorithms for nonlinear network consensus protocols

Cited by 28 publications

References 26 publications

Robust Consensus for Continuous-Time Multiagent Dynamics

Robust Consensus for Continuous-Time Multiagent Dynamics

Lyapunov-based semistability analysis for discrete-time switched network systems

Algebraic criteria for second-order global consensus in multi-agent networks with intrinsic nonlinear dynamics and directed topologies

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