Optimal control of first-order multi-agent systems with leaders

This paper considers optimal control for the first-order multi-agent systems with leaders. Based on linear quadratic regulator theory, we propose a quadratic cost function which is independent of the interaction graph. For the leader-following consensus problem, the optimal control corresponds to a star topology. For the containment control problem, the optimal control is obtained by solving a series of convex optimization problems. Simulation examples are provided to illustrate the effectiveness of the theoretical results.