Finite-time consensus tracking for nonlinear multi-agent systems under undirected and directed communication topologies

This paper addresses the distributed finite-time consensus tracking problem for nonlinear multi-agent systems with external disturbances under fixed undirected and directed communication topologies. A distributed tracking algorithm is proposed, which is based only on the relative information between neighboring agents. By using tools from sliding-mode control theory, it is theoretically shown that the states of the followers can track that of the leader in finite time, if there exists a directed path from the leader to each follower. As a byproduct, some sufficient conditions for finite-time consensus tracking of multi-agent systems without external disturbances are also presented. A numerical example is finally given to illustrate the theoretical results.