Distributed adaptive consensus protocols for multiple Lur'e systems over directed graphs

Abstract

This study addresses the leader–follower consensus problem for multi-agent systems with directed graphs where each agent is modelled as a non-linear Lur'e system. Both the cases where the leader has zero or bounded control inputs are considered. For the case where the leader is of zero control input, a distributed adaptive protocol is designed, under which leader–follower consensus can be achieved for any directed graph containing a directed spanning tree with the leader as the root. For the case where the leader's control input is unknown, but bounded, a novel continuous distributed adaptive protocol is proposed to guarantee the uniform ultimate boundedness of the consensus error and the adaptive coupling gains. The upper bound of the consensus error is also explicitly derived. In comparison to the existing literature, the main contribution of this paper is that the adaptive protocols in this study are fully distributed and meanwhile applicable to a wide class of directed graphs.