A new game model for distributed optimization problems with directed communication topologies

In this paper, the distributed optimization problems of multi-agent systems with directed communication topologies are investigated by using the game theory. In particular, a new general non-cooperative game model, termed state based weakly acyclic game, is provided to solve the problem. Based on this approach, the desired global objective is achieved by designing local objective function for individual agent to make coordination decisions. It is worth noting that all the obtained equilibria are thus solutions to the proposed distributed optimization problems with directed and time-varying communication topologies. Simulations on consensus problem in multi-agent systems are provided to verify the validness of the proposed methodology.