Paper Info
Title
Cluster Consensus with Point Group Symmetries.
Abstract
A cluster consensus system is a multiagent system in which autonomous agents communicate to form groups, and agents within the same group converge to the same point, called the clustering point. We introduce in this paper a class of cluster consensus dynamics, termed G-clustering dynamics for G a point group, in which the autonomous agents can form as many as vertical bar G vertical bar clusters and, moreover, the associated ICI clustering points exhibit a geometric symmetry induced by the point group. The definition of a G-clustering dynamics relies on the use of the so-called voltage graph: a G-voltage graph is a directed graph (digraph) together with a map assigning elements of a group G to the edges of the digraph. For example, in the case when G = {-1, 1}, i.e., the cyclic group of order 2, a voltage graph is nothing but a signed graph. G-clustering dynamics can then be viewed as a generalization of the so-called Altafini's model, which was originally defined over a signed graph, by defining the dynamics over a voltage graph. One of the main contributions of this paper is to identify a necessary and sufficient condition for the exponential convergence of a G-clustering dynamics. Various properties of voltage graphs that are necessary for establishing the convergence result are also investigated, some of which might be of independent interest in topological graph theory.
Year
DOI
Venue
2017
10.1137/16M1070876
SIAM JOURNAL ON CONTROL AND OPTIMIZATION
Keywords
Field
DocType
decentralized systems,cluster consensus,voltage graphs,point groups,exponential convergence
Mathematical optimization,Autonomous agent,Point group,Theoretical computer science,Cluster analysis,Exponential convergence,Homogeneous space,Mathematics
Journal
Volume
Issue
ISSN
55
6
0363-0129
Citations 
PageRank 
References 
0
0.34
0
Authors
3
Name
Order
Citations
PageRank
Xudong Chen19021.40
Mohamed-Ali Belabbas29514.28
Tamer Basar33497402.11