Distributed suboptimal controller synthesis for multi-agent systems

In this paper, the distributed suboptimal LQR control problem for discrete-time multi-agent systems is considered. The distributed controllers that each subsystem can sense and/or exchange information with only a subset of its neighbors are designed, which are based on the topological structure of the system. Using the “averaged” optimization approach, the suboptimal feedback gain matrices are presented and the distributed suboptimal controllers are obtained. Under mild conditions, the asymptotical convergence of the modified Riccati equation is proved. Accordingly, the infinite-time distributed suboptimal controllers are presented. Examples are given to show the efficiency of the proposed results.