Observer-based adaptive controllers for Lur'e multi-agent systems with a dynamic leader

This paper deals with the leader-following consensus problem of Lur'e multi-agent systems (MASs) under undirected topologies, in which the leader has an unknown input. First, based only on the relative outputs among neighbouring agents, a distributed unknown input observer (UIO) is introduced to estimate the relative state of each follower, and the observation errors can exponentially converge to zero. Then, we propose an observer-based discontinuous controller with adaptive gains and demonstrate that the tracking errors can converge to zero. Subsequently, we further propose an observer-based continuous controller with adaptive gains under which chattering phenomenon can be avoided. Unlike the related works, both controllers can achieve leader-following consensus in a fully distributed manner, meaning that they do not depend on the global communication topology structure and the upper bound of the leader's input. Furthermore, two tractable algorithms are devised for computing the gain matrices. Finally, some simulation examples are presented on Chua's circuit system to validate the theoretical results.