This paper investigates the cooperative output regulation for heterogeneous linear multi-agent systems with an uncertain leader under the event-triggered control. Firstly, a local adaptive observer is designed to estimate the system matrices of the leader. Then, utilizing the estimated matrices, an adaptive estimator is proposed to observe the leader’s dynamic behavior and an adaptive regulation law is presented to solve the output regulator equations online. Furthermore, by using the estimated state of the leader and the adaptive solutions of the output regulator equations, a distributed event-triggered controller and a novel self-triggered controller are designed such that the output of each follower can converge the leader’s output, and Zeno behavior can be excluded for each agent. Finally, two numerical simulation examples are provided to verify the effectiveness of the proposed control approaches.

Introduction

Over the past decade, cooperative control for multi-agent systems (MASs) has been a hot topic due to its significant applications in consensus [1]–[۳], flocking [4], [5], formulation [6], [7] and so on. However, the nodes in the most of the previous literatures are assumed to be homogeneous. In fact, the agents have distinct system matrices and even different state dimensions, that is heterogeneous, such as in [8]. Therefore, it is more worthy of studying the heterogeneous MASs. A fundamental problem of the heterogeneous MASs is cooperative output regulation problem whose aim is to make the output of each follower track the reference input or the disturbance generated by the so-called leader. In [9], the cooperative output regulation problem for heterogeneous linear multi-agent systems is investigated in the presence of communication constraints which include intermittent and asynchronous discrete-time information exchange and unknown time-varying delays and possible information losses. Nevertheless, the leader’s system matrices R and S are usually unknown to the followers, that is, the followers cannot directly utilize the leader’s system matrices R and S. It becomes the first important issue to estimate the leader’s system matrices.