Distributed Convex Optimization Over Nonlinear Networks Under Set Constraints

This article is devoted to the distributed convex optimization problem for a class of nonlinear multiagent systems under set constraints. The optimization objective function is composed of the cost function of each agent, where the individual cost function is only accessible by itself. Due to the complexity of nonlinear dynamics of agents, it is very difficult to solve the optimization problem directly. Therefore, we first propose an auxiliary system for each agent, which is used to seek the solution of the global optimization problem. And we present a novel method to ensure that the states of the auxiliary systems are uniformly bounded. Then, a distributed control protocol is designed for the multiagent systems to enable each agent to track its auxiliary system. It is worthy noting that the auxiliary system and the local tracking controller are coupled and need to be jointly designed. Finally, it is proved that the overall systems are stable and the output of each agent can converge to the solution of the constrained optimization problem. Two examples are provided to validate the effectiveness of the proposed method.