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A double-integrator system for distributed optimization of convex cost functions

In this paper, the distributed optimization problem is investigated under a second-order multi-agent system. In the proposed algorithm, each agent solves the optimization via local computation and information exchange with its neighbors through the communication topology. However, in comparison with the existing second-order distributed optimization algorithms, the proposed algorithm is much simpler due to one coupled information exchange among the agents is reduced. To achieve the optimization, the distributed algorithm is proposed based on the consensus method and the gradient algorithm. The optimal solution of the problem is thus obtained with the design of Lyapunov function and the help of LaSallel's Invariance Principle. A numerical simulation example and comparison of proposed algorithm with existing works are presented to illustrate the effectiveness of the theoretical result.