Cluster synchronization of coupled systems with nonidentical linear dynamics

Summary This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly correlated if static couplings are used for all individua...

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Bibliographic Details
Published in:International journal of robust and nonlinear control 2017-06, Vol.27 (9), p.1462-1479
Main Authors: Liu, Zhongchang, Wong, Wing Shing, Cheng, Hui
Format: Article
Language:English
Subjects:
cluster synchronization
Clusters
Computer simulation
coupled linear systems
Couplings
graph topology
Harmonic oscillators
Lower bounds
nonidentical systems
Oscillators
Ships
Synchronism
Weighting
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Summary:Summary This paper considers the cluster synchronization problem of generic linear dynamical systems whose system models are distinct in different clusters. These nonidentical linear models render control design and coupling conditions highly correlated if static couplings are used for all individual systems. In this paper, a dynamic coupling structure, which incorporates a global weighting factor and a vanishing auxiliary control variable, is proposed for each agent and is shown to be a feasible solution. Lower bounds on the global and local weighting factors are derived under the condition that every interaction subgraph associated with each cluster admits a directed spanning tree. The spanning tree requirement is further shown to be a necessary condition when the clusters connect acyclically with each other. Simulations for two applications, cluster heading alignment of nonidentical ships and cluster phase synchronization of nonidentical harmonic oscillators, illustrate essential parts of the derived theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.
ISSN:1049-8923
1099-1239
DOI:10.1002/rnc.3811