Brief paper: Synchronization of coupled harmonic oscillators in a dynamic proximity network

Authors:
Housheng Su;Xiaofan Wang;Zongli Lin
Affiliations:
Department of Automation, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240, China;Department of Automation, Shanghai Jiao Tong University, Dongchuan Road 800, Shanghai 200240, China;Charles L. Brown Department of Electrical and Computer Engineering, University of Virginia, P.O. Box 400473, Charlottesville, VA 22904-4743, USA
Venue:
Automatica (Journal of IFAC)
Year:
2009

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Abstract

In this paper, we revisit the synchronization problems for coupled harmonic oscillators in a dynamic proximity network. Unlike many existing algorithms for distributed control of complex dynamical networks that require explicit assumptions on the network connectivity, we show that the coupled harmonic oscillators can always be synchronized, without imposing any network connectivity assumption. Moreover, we also investigate the synchronization with a leader and show that all harmonic oscillators can asymptotically attain the position and velocity of the leader, again without any assumption on connectivity of the followers. Numerical simulation illustrates the theoretical results.