Consensus for multi-agent dynamic systems: An LQR perspective

This paper considers the optimal consensus problem for interconnected systems consisting of general linear time-invariant dynamics. A linear quadratic regulator (LQR) cost function is proposed which penalizes mutual difference between the states of these subsystems. A distributed control design method is presented which requires the solution of a single LQR problem, and then the LMI-based scheme is used to achieve the optimal performance. The idea behind the method is to adjust the structure of the solution of the algebraic Riccati equation (ARE) according to the structure of the weight matrix of the LQR control problem in such a way that it yields an optimal feedback. It is revealed that the structure of the optimal control law, the weighting matrix of the LQR control problem and the solution of the ARE represent some structure similarity. A numerical example is given to illustrate the effectiveness of the proposed method.