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Optimal containment preview analysis and distributed design for multi-agent systems with general continuous-time linear dynamics and directed acyclic communication topology are considered. Firstly, the state augmentation technique and topology reconstruction method are applied to formulate the original problem as a set of internal-model based local optimal output regulation problem. Secondly, the linear superposition principle is employed to obtain the preview feed-forward compensations corresponding to multiple leaders. Thirdly, by expressing each preview compensation term as a form about the current state of the leader, the solvability of the local optimal output regulation problem, as well as the optimal regulation problems, are proved. On this basis, the sufficient conditions and the distributed optimal control strategy are derived, which ensure the convergence of the containment preview problem. Finally, the effectiveness of the distributed design is illustrated by a numerical experiment.

Optimal containment preview control for continuous-time multi-agent systems using internal model principle