Distributed multiple-bipartite consensus in networked Lagrangian systems with cooperative-competitive interactions

Abstract

In combination with the collective behavior evolutions of bipartite consensus and cluster/group consensus, this paper proposes the notion of multiple-bipartite consensus in networked Lagrangian systems (NLSs). The distributed leaderless and leader-following multiple-bipartite consensus control laws for NLSs are presented in the cooperative-competitive network, where the negative interactions between agents can exist in the same subnetwork. By introducing an acyclic partition and adding the integral item in the control protocols, the final explicit convergence states in the leaderless case are eventually obtained. Moreover, the leader-following scenario can be realized in fifinite time with integrated controllers. All of the effectiveness has been illustrated through numerical simulations.