Distributed adaptive event-triggered protocols for directed multi-agent networks with a dynamic leader of nonzero input

This article addresses the distributed tracking control problem of multi-agent systems with a dynamic leader of nonzero input and under a general graph having a directed spanning tree. According to general engineering request, the communication frequency and the update frequency are often restricted, and the eigenvalue information associated with the topology matrix is probably hard to obtain. Aiming at such a kind of typical control problems, this article proposes an adaptive state feedback event-triggered protocol, including an adaptive controller based on zero-order hold for each follower to ensure the achievement of the tracking task and a dynamic event-triggering condition for each agent to determine when to carry out communications and execute controllers. The proposed protocol guarantees that the tracking error asymptotically converges to zero and there exists no undesirable Zeno behavior, without requiring any eigenvalue information of Laplacian matrix. For the case where local state information is inaccessible, this article designs a state observer based on the local output and further extends to design an adaptive output feedback event-based protocol. In addition to giving strict theoretical proof of the obtain results, this article also verifies the effectiveness of the designed protocols by giving two simulation examples. Compared with the existing related works studying distributed tracking control, it is the main contribution of the current paper that the presented protocols only require a mild connectivity condition on the network topology, and need low frequency control update and information interaction.