Distributed Optimal Leader-Follower Consensus LQR Protocol Design for a Class of High Order Multi-Agent Systems under Time-Varying Topology Approach

In this paper, a leader-follower consensus of multi-agent systems under time-varying undirected communication topology is presented. The dynamics of each agent including the followers and their corresponding leader are considered as linear high order systems. Moreover, the communication topology between the agents and their neighbors depends upon bounded and time-varying functions. To tackle this problem, a set of time-varying distributed Linear Quadratic Regulator (LQR) controller laws for each follower are designed, based on algebraic graph theory and algebraic Riccati equation. The predefined gain and phase margin are both guaranteed in the proposed methodology. Simulation results indicate the effectiveness of the proposed method and display convergence to consensus is achieved in a finite time via time-varying distributed control laws.