Leader–follower consensus for multi-agent systems with three-layer network framework and dynamic interaction jointly connected topology

This paper addresses the leader–follower consensus for linear and nonlinear multi-agent systems with three-layer network framework and dynamic interaction jointly connected topology. By introducing a novel concept of mirroring nodes for different roles of evolution agents, we remove the general assumptions that the topology among followers is specific and continuously contains a spanning tree, and propose a simple criterion to determine if a network is of three-layer framework. This criterion divides the agents of systems into leader-layer, middle-layer and follower-layer nodes according to their functions in cooperative behaviors. Moreover, by combining the state information of agents in different layers, two classes of linear and nonlinear leader–follower consensus protocols are designed with bounded consensus speed. In the sense of Lyapunov stability, it is proved that the leader–follower consensus for the closed-loop linear and nonlinear multi-agent systems can be achieved by employing novel error forms that decouple the leader–follower consensus errors of the three-layer network framework. Two simulation examples are presented to verify the proposed approach and demonstrate its effectiveness.