Group consensus of multi-agent networks with hybrid interactions

Abstract

This paper addresses the issue of group consensus for a novel network model, which possesses a two-layer structure and consists of multiple interactive agents. Agents in the network are divided into several different groups according to hybrid interactions, then two neighboring agents can belong to the same group, different groups but in the same layer or different layers. Correspondingly, three kinds of relationships exist between neighboring agents in the network. Furthermore, consider that only agents in the first layer are pinned by virtual leaders, then based on the graph theory, Lyapunov function method, and optimization technique, some criteria for realizing group consensus of the network under fixed topology and switching topologies are established, which mainly depend on the topology and time intervals of the switching signal. It is found out that when the group consensus is achieved, the agents in the first layer follow the leaders asymptotically, while the agents in the second layer converge to opposite states of the leaders. Finally, a detailed numerical example is given for illustration.