Cooperative optimal control for descriptor multi-agent systems

Abstract

This paper provides a theory analysis of cooperative optimal control problem for leader-follower descriptor multi-agent systems. Based on the linear quadratic regulator theory, the state feedback controller is designed to guarantee the consensus of multi-agent systems and minimize a local performance index, which is independent of the graph topology, the control gain matrix is obtained by solving a generalized Riccati equation. Because the local optimal protocol devised cannot guarantee the global optimality of the entire system, the inverse optimal control theory is applied to design distributed control protocols that ensure consensus and global optimality with respect to some global performance index. The defined performance index is related to the interaction topology, whose Laplacian matrix is constrained to be diagonalizable. Finally, two numerical examples and comparisons are supplied to verify the effectiveness of the theoretical results.