Distributed Optimal Consensus Control Algorithm for Continuous-Time Multi-Agent Systems

This brief proposes a distributed algorithm to solve the optimal consensus control problem of continuous-time multi-agent systems. With the definition of consensus manifold, the utility function of the optimization problem is formulated as a linear quadratic polynomial which indicates the tradeoff between convergence rate and energy cost in a finite horizon. Applying the alternating direction method of multiplier, the optimal consensus problem is separated into three subproblems: 1) an input optimization problem; 2) a consensus state optimization problem; and 3) a dual optimization problem, thereby separating the communication topology and the agents dynamics. Then, these subproblems can be analyzed and solved independently, following from which that a distributed control algorithm is proposed to allow the continuous-time multi-agent systems to reach optimal consensus. A numerical example is given to demonstrate the effectiveness of the proposed algorithm.