Leader-follower consensus for high-order integrator systems with Lipschitz nonlinear dynamics

This paper considers the leader-follower consensus problem of multi-agent systems with Lipschitz nonlinear dynamics under directed communication topology. The state of the leader is only available to a subset of the followers and the input of the leader is nonzero and unknown to any of the follower. Based on relative states of neighboring agents, a distributed adaptive nonlinear protocol is proposed for each follower. It is proved that, for any directed communication graph that contains a spanning tree with the root node being the leader agent, the protocol ensures that the states of the followers converge to the state of the leader. Moreover coupling weights converge to some finite values. Compared with some existing results in the literature, the adaptive consensus protocols here can be implemented by each agent in a fully distributed fashion without using any global information. A simulation example is provided to illustrate the theoretical results.