A Novel Approach to Prescribed-Time Cooperative Output Regulation in Linear Heterogeneous Multi-Agent Systems Using Cascade System Criteria

This paper investigates the prescribed-time cooperative output regulation (PTCOR) for a class of linear heterogeneous multi-agent systems (MASs) under directed communication graphs. As a special case of PTCOR, the necessary and sufficient condition for prescribed-time output regulation of an individual system is first explored, whereas only sufficient conditions are developed in the literature. A PTCOR algorithm is subsequently developed, composed of prescribed-time distributed observers, local state observers, and tracking controllers, utilizing a distributed feedforward method. This approach converts the PTCOR problem into the prescribed-time stabilization problem of a cascaded subsystem. The criterion for the prescribed-time stabilization of the cascaded system is proposed, differing from that of traditional asymptotic or finite-time stabilization of a cascaded system. It is proven that the regulated outputs converge to zero within a prescribed time and remain at zero afterward, while all internal signals in the closed-loop MASs are uniformly bounded. Finally, the theoretical results are validated through two numerical examples.