Consensus in Multi-Agent Systems With Coupling Delays and Switching Topology

Münz, Ulrich; Papachristodoulou, Antonis; Allgöwer, Frank

doi:10.1109/tac.2011.2161052

Cited by 218 publications

(121 citation statements)

References 30 publications

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“…For bidirectional and "cutbalanced" graphs necessary and sufficient consensus criteria have been obtained [9]- [11]. At the same time, for general directed graph convergence to consensus is proved under the sufficient (but not necessary) assumption of "uniform quasistrong connectivity (UQSC)" [5]- [7].…”

Section: X(t) = −L(t)x(t)mentioning

confidence: 98%

“…Proskurnikov is with the ENTEG institute at the University of Groningen, The Netherlands and also with St. Petersburg State University, ITMO University and Institute for Problems of Mechanical Engineering (IPME RAS), St. Petersburg, Russia; avp1982@gmail.com M. Cao is with the ENTEG institute at the University of Groningen, The Netherlands; m.cao@rug.nl where x(t) stands for the vector of agents' states x i (t) ∈ R and L(t) is the Laplacian matrix [1], [2] of their interaction graph (in general, directed and weighted). This protocol and its discrete-time counterpart has been thoroughly studied by using Lyapunov methods [5]- [7] and matrix analysis [1], [2], [8], paying special attention to the effects of timevarying interaction topologies. For bidirectional and "cutbalanced" graphs necessary and sufficient consensus criteria have been obtained [9]- [11].…”

Section: X(t) = −L(t)x(t)mentioning

confidence: 99%

“…The case of cut-balanced ISC graph is proved in [9] (alternative proofs can be found in [10], [11]). The case of UQSC graph is usually examined under the assumption of piecewise-continuous Laplacian with positive dwell time between consecutive switches [1], [6], [7]. The proof in the general situation is beyond the scope of this paper.…”

Section: Lemma 1: Suppose the Graph G[a(t)]mentioning

confidence: 99%

See 2 more Smart Citations

Dichotomic differential inequalities and multi-agent coordination

Proskurnikov

Cao

2016

2016 European Control Conference (ECC)

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Abstract-Distributed algorithms of multi-agent coordination have attracted substantial attention from the research communities. The most investigated are Laplacian-type dynamics over time-varying weighted graphs, whose applications include, but are not limited to, the problems of consensus, opinion dynamics, aggregation and containment control, target surrounding and distributed optimization. While the algorithms solving these problems are similar, for their analysis different mathematical techniques have been used. In this paper, we propose a novel approach, allowing to prove the stability of many Laplacian-type algorithms, arising in multi-agent coordination problems, in a unified elegant way. The key idea of this approach is to consider an associated linear differential inequality with the Laplacian matrix, satisfied by some bounded outputs of the agents (e.g. the distances to the desired set in aggregation and containment control problems). Although such inequalities have many unbounded solutions, under natural connectivity conditions all their bounded solutions converge (and even reach consensus), entailing the convergence of the original protocol. The differential inequality thus admits only convergent but not "oscillatory" bounded solutions. This property, referred to as the dichotomy, has been long studied in the theory of differential equations. We show that a number of recent results from multi-agent control can be derived from the dichotomy criteria for Laplacian differential inequalities, developed in this paper, discarding also some technical restrictions.

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Section: X(t) = −L(t)x(t)mentioning

confidence: 98%

Section: X(t) = −L(t)x(t)mentioning

confidence: 99%

Section: Lemma 1: Suppose the Graph G[a(t)]mentioning

confidence: 99%

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Dichotomic differential inequalities and multi-agent coordination

Proskurnikov

Cao

2016

2016 European Control Conference (ECC)

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“…Definition 1 (Uniformly Quasi-Strongly Connected [7]): A switching graph ( ) is uniformly quasi-strongly connected if there is a > 0 such that for all ≥ 0, the union graph [ , + ) is quasi-strongly connected, i.e., [ , + ) contains a spanning tree.…”

Section: A Problem Formulationmentioning

confidence: 99%

Synchronisation of linear continuous multi‐agent systems with switching topology and communication delay

Xiang

Wei

et al. 2014

IET Control Theory & Applications

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A distributed dynamic output feedback control is designed by Scardovi and Sepulchre for the synchronization of a network of identical linear systems, known as agents in literature. The design is based on some mild conditions allowing switching topology. But it assumes that there is no time delay in signal transfer between the neighbouring agents. In this paper we extend their work to include known time delay in communications. Furthermore, our design has some special features: (a) the delay can be arbitrary and only need to be uniformly bounded by a constant, (b) the conditions that time delay should be the same and sufficiently small in some literature are not required here, and (c) no local buffer is required to store past data due to time-delay effect.

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“…The practical applications of consensus are diverse and can be found in many fields, such as biology, physics, control systems, and robotics [5][6][7][8][9][10][11]. The consensus problem was first discussed for first order [12][13][14][15] and then generalized to second order [16,17], general linear dynamics [18,19], and nonlinear dynamics [20,21] in communication networks and sensor networks.…”

Section: Introductionmentioning

confidence: 99%

Consensus of Switched Multiagent Systems under Relative State Constraints

Wang

2017

Complexity

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The consensus problem is presented for the switched multiagent system (MAS), where the MAS is switched between continuousand discrete-time systems with relative state constraints. With some standard assumptions, we obtain the fact that the switched MAS with relative state constraints can achieve consensus under both fixed undirected graphs and switching undirected graphs. Furthermore, based on the absolute average value of initial states, we propose sufficient conditions for consensus of the switched MAS. The challenge of this study is that relative state constraints are considered, which will make the consensus problem much more complex. One of the main contributions is that, for the switched MAS with relative state constraints, we explore the solvability of the consensus problem. Finally, we present two simulation examples to show the effectiveness of the results.

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Consensus in Multi-Agent Systems With Coupling Delays and Switching Topology

Cited by 218 publications

References 30 publications

Dichotomic differential inequalities and multi-agent coordination

Dichotomic differential inequalities and multi-agent coordination

Synchronisation of linear continuous multi‐agent systems with switching topology and communication delay

Consensus of Switched Multiagent Systems under Relative State Constraints

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