Cooperative–Competitive Multiagent Systems for Distributed Minimax Optimization Subject to Bounded Constraints

This paper presents continuous-time multiagent systems for distributed minimax optimization subject to bounded constraints. All agents in the system are divided into two groups for minimization and maximization. The multiagent system features competitive intergroup interactions and cooperative intragroup interactions, both of which are based on the output information of agents. First, a proportional-integral (PI) intragroup interaction rule is utilized for consensus within each group in the system. With this interaction rule, the system is proved to be convergent to an optimal solution to the problem, under a certain requirement on the intergroup interactions. Second, another discontinuous intragroup interaction rule is introduced. It is proved that the system with such an interaction is still convergent to an optimal solution if the proportional gain exceeds a derived lower bound, without the previous requirement on the intergroup interactions. As a special case, the systems are further applied for distributed optimization. Finally, simulation results are presented to substantiate the theoretical results.