Synchronization of coupled harmonic oscillators with local instantaneous interaction

• Published in: Automatica (Oxford) Vol. 48; no. 8; pp. 1715 - 1721
• Main Authors: Zhou, Jin, Zhang, Hua, Xiang, Lan, Wu, Quanjun
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-08-2012; Elsevier
• Subjects: Algorithms; Applied sciences; Artificial intelligence; Collaborative systems; Computer science; control theory; systems; Computer systems and distributed systems. User interface; Convergence; Coupled harmonic oscillators; Exact sciences and technology; Harmonic oscillators; Instantaneous interaction; Multi-agent systems; Networks; Oscillators; Software; Switching theory; Synchronism; Synchronization; Instantaneous interaction; Coupled harmonic oscillators; Synchronization; Collaborative systems; Multi-agent systems; Interconnection network; Multimodel control; Packet switching; Coupled oscillator; Distributed system; Multiagent system; Network topology; Graph connectivity; Efficiency; Distributed algorithm; Feasibility; Artificial intelligence; Algorithm analysis; Numerical convergence; Information exchange; Harmonic oscillator; Switching networks
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2012.05.022

In this brief we propose a distributed algorithm for synchronization of coupled harmonic oscillators with local instantaneous interaction. We provide convergence analysis for such algorithm without and with a leader over fixed and switching undirected network topologies, respectively. We also establish the conditions by which the coupled harmonic oscillators achieve synchronized oscillatory motions under instantaneous network connectivity. It is shown that the coupled harmonic oscillators can be synchronized even each oscillator instantaneously exchanges the velocity information with its neighbors only at discrete moments. Subsequently, numerical examples illustrate and visualize the effectiveness and feasibility of the theoretical results.