Sample-based Zero-Gradient-Sum distributed consensus optimization of multi-agent systems

This paper addresses distributed convex optimization problem for continuous-time multi-agent systems via sampled control over undirected networks. A novel sampled-based Zero-Gradient-Sum (ZGS) distributed optimization algorithm is proposed which are induced from ZGS algorithm by using periodic sampling technology and zero-order hold circuit. A new Lyapunov-based approach is used to give convergence analysis of the proposed algorithm. By choosing proper sampling period and gain parameter, we prove that each agent of the system converges asymptotically to the unknown optimal value of the cost function. A simulation example is given to illustrate the effectiveness of the algorithm proposed in this paper.