Stability of leaderless discrete-time multi-agent systems

Angeli, David; Bliman, Pierre‐Alexandre

doi:10.1007/s00498-006-0006-0

Cited by 85 publications

(57 citation statements)

References 23 publications

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“…To attain generality, we consider convexity in metric spaces more general than the standard Euclidean space, where line segments are replaced by geodesic segments but preserving the very essential property of their counterparts in R n : being the unique shortest path between two points. In that respect, the generalization of the analysis here is seemingly different from the generalization in [7], but we defer comparison for later.…”

Section: Introductionmentioning

confidence: 87%

“…The relaxation allows working with sets that are not necessarily convex but are transformable (via some invertible map) to convex sets. Both [6] and [7] establish only qualitative convergence results.…”

Section: Introductionmentioning

confidence: 89%

“…Two particular papers to which the current work is closely related are [6] and [7]. Moreau shows in [6] that states of all agents evolve toward a consensus by converging to a common point if the following assumptions hold:…”

Section: Introductionmentioning

confidence: 99%

“…His work is generalized in [7] where the convexity property in (a) is relaxed. The relaxation allows working with sets that are not necessarily convex but are transformable (via some invertible map) to convex sets.…”

Section: Introductionmentioning

confidence: 99%

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Consensus under general convexity

Tuna

Sepulchre

2007

2007 46th IEEE Conference on Decision and Control

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Abstract-A method is proposed to characterize contraction of a set through orthogonal projections. For discrete-time multi-agent systems, quantitative estimates of convergence (to a consensus) rate are provided by means of contracting convex sets. Required convexity for the sets that should include the values that the transition maps of agents take is considered in a more general sense than that of Euclidean geometry.

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Section: Introductionmentioning

confidence: 87%

Section: Introductionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Consensus under general convexity

Tuna

Sepulchre

2007

2007 46th IEEE Conference on Decision and Control

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“…Tsitsiklis et al also provided important qualitative contributions to this subject [20,21,3], as well as Moreau [15]. See also [1] for further nonlinear results. In particular, the role of connectivity of the communication graph in the convergence of consensus and spanning trees has been recognised and finely analysed [15,5,16].…”

Section: Introductionmentioning

confidence: 95%

Tight estimates for convergence of some non-stationary consensus algorithms

Angeli

Bliman

2008

Systems & Control Letters

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The present paper is devoted to estimating the speed of convergence towards consensus for a general class of discrete-time multi-agent systems. In the systems considered here, both the topology of the interconnection graph and the weight of the arcs are allowed to vary as a function of time. Under the hypothesis that some spanning tree structure is preserved along time, and that some nonzero minimal weight of the information transfer along this tree is guaranteed, an estimate of the contraction rate is given. The latter is expressed explicitly as the spectral radius of some matrix depending upon the tree depth and the lower bounds on the weights.

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Consensus in Multi‐Agent Systems

Proskurnikov

Cao

2016

Wiley Encyclopedia of Electrical and Electronics Engineering

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Many cooperative behaviors of multi‐agent teams emerge from local interactions among the agents, where an agent interacts with a few “adjacent” teammates, but has no information about the remaining agents. For instance, the self‐organization of many biological populations –including swarms of insects, flocks of birds, and schools of fish –are based on such local interaction rules: the motion and decisions of an individual agent are determined by the behavior of its nearest neighbors in the population. A special case of multi‐agent coordination is consensus , that is, the agreement of agents on some quantity of interest or, more generally, the full or partial synchronization of their state trajectories. Establishing consensus is a “benchmark” problem in multi‐agent systems study, which allows to reveal the main principles of multi‐agent coordination and, in particular, the role of the system's interaction graph (or topology). Consensus lies in the heart of many natural phenomena (e.g., synchronous oscillation of neural cells, which maintains a stable heart rhythm) and engineering designs (e.g., attitude synchronization of satellites). In this article, we give a brief review of distributed consensus algorithms, focusing on the basic ideas and relevant mathematical theory, in particular, graph‐theoretic methods.

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Stability of leaderless discrete-time multi-agent systems

Cited by 85 publications

References 23 publications

Consensus under general convexity

Consensus under general convexity

Tight estimates for convergence of some non-stationary consensus algorithms

Consensus in Multi‐Agent Systems

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