Different Types of Distributed Optimal Leader-Follower Consensus Protocol Design for a Class of High-Order Multi-Agent Systems

Different types of optimal leader-follower consensus of high-order multi-agent systems (MAS) under fixed, connected, and directed communication topology are presented in this paper. The dynamics of each agent including the followers and their corresponding leader is a linear high order system. First, the Linear Quadratic Regulator (LQR) problem is discussed to achieve the optimal consensus for high-order linear MAS with a guaranteed predefined phase and gain margin. Then stochastic leader-follower consensus problem of MAS in the presence of the Gaussian noise is designed. To tackle these problems, a set of fixed distributed control laws for each follower agent is designed, based on algebraic graph theory. Simulation results indicate the effectiveness of the proposed method and display the consensus in both cases via distributed control laws.