Finite-time distributed global optimal control for linear time-varying multi-agent systems: a dynamic output-feedback perspective

This study presents a systematic procedure to solve the problem of finite-time distributed global optimal control for the leaderless and leader-follower homogeneous multi-agent systems (MASs). Each agent's dynamics is given in general form of continuous-time linear time-varying (LTV) systems. The communication network among the agents is also assumed to be undirected and directed under fixed topology. First, based on asymptotic stability principle, inverse optimal results of general LTV systems are constructed. Second, the necessary and sufficient conditions are given for the existence of the distributed optimal state feedback and optimal dynamic output feedback control that solves a global optimal control problem for MASs. Then, the sufficient condition for finite-time stability of both the state and the output feedback problems for MASs are stated. Finally, some numerical example results are provided to illustrate the effectiveness and applicability of the proposed scheme.