Cluster consensus of heterogeneous linear multi-agent systems

Abstract

This study addresses the cluster consensus problem for generic linear heterogeneous multi-agent systems. The main purpose of this study is to unveil how agents confront the effects of intra-cluster couplings and inter-cluster couplings, and reach cluster consensus. For the semi-heterogeneous case, where agents in the same cluster have identical dynamics, cluster consensus is achieved if each agent suppresses the inter-cluster couplings. For the heterogeneous case, where all agents have different dynamics, cluster consensus is achieved if each agent confronts both inter-cluster and intra-cluster couplings. Two kinds of control protocols using relative output errors are designed for the heterogeneous case. For both semi-heterogeneous and heterogeneous cases, design procedures are provided to construct controllers to satisfy the relation between the dynamics of agents and the communication graph, which ensure cluster consensus. Finally, numerical examples are provided to verify the theoretical results.