A Continuous-time Algorithm with the Sigmoid Function for Distributed Constrained Optimization of Multi-agent Systems

We study the distributed optimization problem with constraint sets in continuous-time multi-agent systems (MAS). The local cost function of each agent is strictly convex in the feasible region and agents can exchange state information with neighbors over an undirected graph. All agents cooperatively reach the state which minimizes the sum of agents' cost functions and achieves consensus satisfying constraint sets. Based on penalty function methods combined with KKT condition and projection technique, a distributed continuous-time control law is designed. By Lyapunov stability theory and LaSalles invariance principle, the states of all agents converging to the global optimum from any initial state is analyzed. Finally, the performance of the proposed algorithm is verified by a numerical example.