Optimal Time-Varying Formation Tracking Control for Second-Order Swarm Systems Based on LQR Method

This paper deals with optimal time-varying formation tracking control problems for second-order swarm systems, where the formation tracking performance as well as the energy consumption are considered. First, an objective optimization function integrated tracking performance index, collaborative energy consumption index and tracking energy consumption index is proposed to impose restriction on the design of the controller. Afterwards, by establishing the formation tracking error differential equation of the swarm system and taking a non-singular transformation, it turns into a linear quadratic regulator (LQR) optimal control problem. Hence, the optimal controller is obtained by solving Riccati equation, where the controller only requires that the communication topology of the swarm system is undirected and connected, and the specific minimum value of the objective optimization function is subsequently derived. At last, a numerical simulation example is constructed to demonstrate the effectiveness of the optimal controller.