Adaptive cluster synchronisation of coupled harmonic oscillators with multiple leaders
- Author(s): Housheng Su 1 ; Michael Z. Q. Chen 2 ; Xiaofan Wang 3 ; Hongwei Wang 1 ; Najl V. Valeyev 4
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View affiliations
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Affiliations:
1:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Key Laboratory of Education Ministry for Image Processing and Intelligent Control, Wuhan 430074, People's Republic of China;
2: Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, People's Republic of China;
3: Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China;
4: College of Engineering, Mathematics and Physical Sciences, University of Exeter, Exeter, UK
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Affiliations:
1:
Department of Control Science and Engineering, Huazhong University of Science and Technology, Key Laboratory of Education Ministry for Image Processing and Intelligent Control, Wuhan 430074, People's Republic of China;
- Source:
Volume 7, Issue 5,
21 March 2013,
p.
765 – 772
DOI: 10.1049/iet-cta.2012.0910 , Print ISSN 1751-8644, Online ISSN 1751-8652
In this study, the authors investigate the cluster synchronisation of coupled harmonic oscillators with multiple leaders in an undirected fixed network. Unlike many existing algorithms for cluster synchronisation of complex dynamical networks or group consensus of multi-agent systems, which require global information of the underlying network such as eigenvalues of the coupling matrix or centralised control protocols, we propose a novel decentralised adaptive cluster synchronisation protocol for coupled harmonic oscillators. By using the decentralised adaptive cluster synchronisation protocol and without using any global information of the underlying network, all oscillators in the same group asymptotically synchronise with the corresponding leader even when only one oscillator in each group has access to the information of the corresponding leader. Numerical simulation results are presented to illustrate the theoretical results.
Inspec keywords: eigenvalues and eigenfunctions; synchronisation; multi-robot systems; decentralised control; harmonic oscillators; matrix algebra; adaptive control
Other keywords: group consensus; global information; centralised control protocol; decentralised adaptive cluster synchronisation protocol; coupling matrix; eigenvalue; multiple leaders; multiagent system; coupled harmonic oscillators; undirected fixed network; numerical simulation; complex dynamical network; information access
Subjects: Robotics; Linear algebra (numerical analysis); Multivariable control systems; Self-adjusting control systems
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