Design and analysis of distributed optimal controller for identical multiagent systems

Abstract

This paper studies the optimal distributed control design problem for both continuous-time and discrete-time systems. We consider an identical decoupled dynamical system and a coupled performance index which is described through the Laplacian matrix. It is showed that the optimal feedback gain matrix corresponds to a complete undirected graph for the Laplacian matrix in the cost function. We aim to get the distributed controllers that only use the information of its state and the states of its neighbors. The existence conditions of the optimal distributed control for special cost function are given and the asymptotic stability of the system is discussed. Examples are given to show the efficiency of the proposed results.