An Accelerated Algorithm for Linear Quadratic Optimal Consensus of Heterogeneous Multi-Agent Systems

An accelerated algorithm is proposed in this paper for solving the linear quadratic optimal consensus problem of multi-agent systems. To optimize the linear quadratic response and the final consensus state simultaneously, a nonseparable multi-objective optimization problem with coupled constraints on decision variables is formulated. The main difficulty in solving the optimization problem lies in the nonlinear coupling of objectives, which is overcome by separating the problem into two independent and solvable single-objective optimization subproblems using the alternating direction method of multipliers. The proximal gradient decent scheme is then introduced to approximate the precise optimal solutions of the subproblems so as to improve the computing efficiency. Convergence analysis is performed to estimate the convergence rate and derive the convergence condition, which is independent of any global information of the system and therefore is fully distributed. Furthermore, the solution of each subproblem is obtained in a distributed form, allowing the multi-agent system to achieve optimal consensus. Numerical examples show the effectiveness of the accelerated algorithm.