Adaptive group consensus of coupled harmonic oscillators with multiple leaders

In this paper, we investigate the group consensus of coupled harmonic oscillators with multiple leaders in an undirected fixed network. Unlike many existing algorithms for group consensus of multi-agent systems or cluster synchronization of complex dynamical networks, which require global information of the underlying network such as the eigenvalues of the coupling matrix or centralized control protocols, we propose a novel decentralized adaptive group consensus algorithm for coupled harmonic oscillators. By using the decentralized adaptive group consensus algorithm and without using any global information of the underlying network, all agents in the same group asymptotically synchronize with the corresponding leader even when only one agent in each group has access to the information of the corresponding leader. Numerical simulation results are presented to illustrate the theoretical results.