Fully Distributed Cooperative Output Regulation of Heterogeneous Periodic Linear Multi‐Agent Systems With Input Saturation

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ABSTRACTThis article delves into the cooperative output regulation of heterogeneous continuous‐time periodic linear multi‐agent systems with input saturation under undirected graphs. Leveraging characteristics inherent in the parametric differential Lyapunov equation and cooperative output regulation theory, we formulate an observer‐based protocol. Specifically, we design distributed state observers for both the leader and followers, aiming to estimate the leader state and the follower state itself, respectively. Utilizing these estimated states, we propose a class of fully distributed observer‐based protocols to address the considered problem. In addition, we make an extension to the reduced‐order observer‐based form. The most distinguishing contributions of our proposed protocols, in contrast to existing literature, lie in the fact that the considered dynamics of each agent are time‐varying and have input saturation constraints. Notably, our protocols eliminate the need for global information of the network, operating in a fully distributed method. Finally, we apply the proposed control protocol to the multi‐spacecraft elliptical orbit rendezvous problem.