The research of distributed suboptimal controller for continuous-time multi-agent systems

This paper revisits the distributed suboptimal LQR control problem for continuous-time multi-agent systems. Based on the system's topological structure, we design the distributed controllers in which each subsystem can use the information of its state and its neighbors'. The multi-agent system are described by an identical decoupled dynamical equation and a coupled performance index. Associating with the given matrix G and the designed suboptimal feedback gain matrices, the general distributed suboptimal controllers are obtained. By using the stable eigenvectors of the Hamiltonian matrix, the asymptotical convergence of the modified ARE is proved for infinite-horizon systems under mild conditions. To make this result more persuasively, the consideration for infinite-time distributed systems is presented and the suboptimal controllers are obtained.