Global leader-following consensus of a group of multiple integrator agents using bounded controls

This paper studies the global leader-following consensus problem for a multi-agent system using bounded controls. Both the agents and the leader are described by a chain of integrators of arbitrary length. A saturated linear feedback control law is constructed for each system in the group. These feedback laws use a multi-hop relay protocol, in which each agent obtains the information of other agents through multi-hop paths in the communication network, and the feedback gains are constructed from the adjacency matrix of the communication network. It is shown that global leader-following consensus is achieved under the feedback control laws we have constructed when the communication topology among follower agents is a strongly connected and detailed balanced directed graph and the leader is a neighbor of at least one follower. Simulation results are given to illustrate the theoretical results.