Cluster consensus in networks of agents with weighted cooperative-competitive interactions via nonlinear protocols

In this paper, we consider the consensus problem of networks of agents with weighted cooperative-competitive interactions via nonlinear protocols. Each agent in the multi-agent system is endowed with a value representing its intrinsic interaction property, based on which, the cooperative-competitive interaction weights are decided. Two types of nonlinear protocols with weighted cooperative-competitive interactions are proposed. By using Lyapunov function method, it is proved that these protocols lead to cluster consensus, and the agents are in the same cluster if and only if their interaction properties are the same. Several numerical examples are presented to demonstrate the effectiveness of the theoretical results.