Cluster consensus for coupled harmonic oscillators under a weighted cooperative-competitive network

Abstract

Cluster consensus is investigated for multiple coupled harmonic oscillators under a weighted cooperative-competitive network. Consensus protocols for three categories of communication networks are constructed by employing a weighted gain, and sufficient conditions for guaranteeing cluster consensus are obtained. It is found that under the proposed protocols, the states of all oscillators can be guaranteed to reach periodic orbits that are the same in frequency no matter which cluster the oscillators belong to. In particular, cluster partitions here are not given a prior, but are determined by the communication topology among oscillators. Numerical examples are given to validate the effectiveness of theoretical results.

Keywords:

• Multi-agent systems
• cluster consensus
• coupled harmonic oscillators
• a weighted cooperative-competitive network

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The work was supported in part by the National Natural Science Foundation of China [grant number 61973183 and 62173317]; the National Key Research and Development Program of China [grant number 2018AAA0100801]; the Natural Science Foundation of Shandong Province [grant number ZR2019MF041]; and the Youth Creative Team Sci-Tech Program of Shandong Universities [grant number 2019KJI007].