A Necessary and Sufficient Condition for Consensus of Continuous-Time Agents Over Undirected Time-Varying Networks

Cao, Lingzhi; Zheng, Yufan; Zhou, Qing

doi:10.1109/tac.2011.2157393

Cited by 53 publications

(29 citation statements)

References 27 publications

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“…In particular, the result from [5] includes those from [2] (using strongly symmetric weights) and [9] (using balanced weights).…”

Section: Related Resultsmentioning

confidence: 99%

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Continuous-Time Consensus under Persistent Connectivity and Slow Divergence of Reciprocal Interaction Weights

Martín¹,

Girard²

2013

SIAM J. Control Optim.

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International audienceIn this paper, we present new results on consensus for continuous-time multiagent systems. We introduce the assumptions of persistent connectivity of the interaction graph and of slow divergence of reciprocal interaction weights. Persistent connectivity can be considered as the counterpart of the notion of ultimate connectivity used in discrete-time consensus protocols. Slow divergence of reciprocal interaction weights generalizes the assumption of cut-balanced interactions. We show that under these two assumptions, the continuous-time consensus protocol succeeds: the states of all the agents converge asymptotically to a common value. Moreover, our proof allows us to give an estimate of the rate of convergence towards the consensus. We also provide examples that make us think that both of our assumptions are tight

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“…In particular, the result from [5] includes those from [2] (using strongly symmetric weights) and [9] (using balanced weights).…”

Section: Related Resultsmentioning

confidence: 99%

“…Consensus algorithms have attracted a lot of attention in the past decade. Notable convergence results include [6,8,10,1,5] for the discrete-time and [9,7,10,5,2,3] for the continuous time consensus algorithm.…”

Section: Introductionmentioning

confidence: 99%

Continuous-Time Consensus under Persistent Connectivity and Slow Divergence of Reciprocal Interaction Weights

Martín¹,

Girard²

2013

SIAM J. Control Optim.

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“…Therefore, the consensus problem has been further investigated (Olfati-Saber and Murray, 2004;Hong et al, 2006;Bliman and Ferrari-Trecate, 2008;Cortés, 2008;Tian and Liu, 2009;Zhu and Cheng, 2010;Cao et al, 2011;Li et al, 2011;Hendrickx and Tsitsiklis, 2013).…”

Section: Consensusmentioning

confidence: 99%

“…A typical case is the consensus problem over a switching topology. That is, the topology switches over time, so is the Laplacian (Lin et al, 2004;Olfati-Saber and Murray, 2004;Ren and Beard, 2004;Moreau, 2005;Cao et al, 2011;Proskurnikov, 2013;Wei and Fang, 2014).…”

Section: Distributed Coordination Over Switching Topologiesmentioning

confidence: 99%

Distributed coordination in multi-agent systems: a graph Laplacian perspective

Han

Lin

et al. 2015

Frontiers Inf Technol Electronic Eng

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This paper reviews some main results and progress in distributed multi-agent coordination from a graph Laplacian perspective. Distributed multi-agent coordination has been a very active subject studied extensively by the systems and control community in last decades, including distributed consensus, formation control, sensor localization, distributed optimization, etc. The aim of this paper is to provide both a comprehensive survey of existing literature in distributed multi-agent coordination and a new perspective in terms of graph Laplacian to categorize the fundamental mechanisms for distributed coordination. For different types of graph Laplacians, we summarize their inherent coordination features and specific research issues. This paper also highlights several promising research directions along with some open problems that are deemed important for future study.

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“…Based on Lemma 1, The stochastic derivative of V along trajectories of system (12) can be expressed as dV (t, e(t)) = LV (t, e(t))dt + 2e T (t) (t)dW (t) (14) where…”

Section: Remarkmentioning

confidence: 99%

Consensus of a leader‐following multi‐agent system with negative weights and noises

Cao

et al. 2014

IET Control Theory & Applications

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This study is concerned with the issue of mean-square consensus for a model of leader-following multi-agent system. The agents acting as followers update states based on the information received from the time varying neighbours and the virtual leader. Negative weights besides positive weights are introduced for the links existing among the agents. Moreover, all followers considered here are influenced by noises with different intensities emerging from the external environment or transmission channels. In order to guarantee consensus of the multi-agent system under the noises, the corresponding sufficient conditions are derived. Theoretical proofs are given mainly by using the Lyapunov function approach and the stochastic analysis. Finally, some numerical examples are presented to demonstrate the effectiveness of the results.

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A Necessary and Sufficient Condition for Consensus of Continuous-Time Agents Over Undirected Time-Varying Networks

Cited by 53 publications

References 27 publications

Continuous-Time Consensus under Persistent Connectivity and Slow Divergence of Reciprocal Interaction Weights

Continuous-Time Consensus under Persistent Connectivity and Slow Divergence of Reciprocal Interaction Weights

Distributed coordination in multi-agent systems: a graph Laplacian perspective

Consensus of a leader‐following multi‐agent system with negative weights and noises

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