Distributed Nash Equilibrium Seeking for Games With Unknown Nonlinear Players via Fuzzy Adaptive Method

In this article,we investigate the distributed Nash equilibrium seeking problem for games with unknown nonlinear players under both event-triggered communication and switching topologies. To be specific, the fuzzy adaptive method is utilized to approximate the unknown nonlinear functions included in the players' dynamics. Under switching topologies, the fully distributed control strategies based on gradient-like optimization method and leader-consensus protocols are developed to solve the distributed Nash equilibrium seeking problem. A novel event-triggered communication protocol based on the local information from neighboring players is designed under switching topologies to reduce the communication burden. With the help of Lyapunov stability theory, it is proved that under the developed control strategies, the players' actions can be driven to the small neighborhood of the Nash equilibrium and the Zeno behavior can be avoided. The effectiveness of the developed algorithms is demonstrated through a numerical example.