Distributed minimum-energy containment control of continuous-time multi-agent systems by inverse optimal control

Dear Editor, This letter focuses on the distributed optimal containment control of continuous-time multi-agent systems (CTMASs) with respect to the minimum-energy performance index over fixed topology. To achieve this, we firstly investigate the optimal containment control problem using the inverse optimal control method, where all states of followers asymptotically converge to the convex hull spanned by the leaders while some quadratic performance indexes get minimized. A sufficient condition for existence of the distributed optimal containment control protocol is derived. By introducing the parametric algebraic Riccati equation (PARE), it is strictly proved that the global performance index can be used to approximate the standard minimum-energy performance index as the parameters tends to infinity. In consequence, the standard minimum-energy cooperative containment control can be solved by local steady state feedback protocols. Finally, numerical examples are given to demonstrate the effectiveness of theoretical results.