LQR-Based Optimal Leader-Follower Consensus of Second-Order Multi-agent Systems

This paper considers an optimal consensus problem of second-order leader-follower multi-agent systems by using inverse optimality and LMI method. For a given control input, under the condition that the communication topology among followers is undirected connected, a positive definite matrix in a linear quadratic performance index function is obtained, which makes the linear quadratic performance index function to obtain the minimum value. Meanwhile, through theory analysis, we prove that the coefficient matrix of the given control input is the optimal feedback gain matrix. The simulation results show the effectiveness of our conclusions.