Distributed optimization problem for double-integrator systems with the presence of the exogenous disturbance

The aim of this paper is to study the distributed optimization problem for continuous-time multi-agent systems with the existence and the interference of external disturbance, therein each agent is described as double-integrator dynamic. To reject the exogenous disturbance, the distributed algorithm is proposed for each agent based on the internal model principle. The proposed algorithm only utilizes the position information of each agent from its neighbors subject to the undirected graph, which can reduce communication costs and energy consumptions in applications. Moreover, the algorithm only needs the cost functions of the agent itself, which can greatly protect the privacy of other agents. The optimal solution of the problem is thus obtained with the design of Lyapunov function and the help of convex analysis, LaSallel's Invariance Principle. Finally, two numerical simulation examples and the comparison of proposed algorithm with other previous research are presented to illustrate the persuasive effectiveness of the theoretical result.