Distributed Nash Equilibrium Seeking for Games with Nonlinear Players via Fuzzy Adaptive Control

This paper explores the distributed Nash equilibrium seeking problem for games involving a class of players with unknown high-order nonlinear dynamics. Firstly, the fuzzy observer is employed to estimate the unknown nonlinearities and unmeasurable states. Next, an observer-based distributed Nash equilibrium seeking algorithm is developed using the fuzzy adaptive backstepping method. The algorithm ensures that the players' actions can be regulated within the neighbourhood of the Nash equilibrium, and all signals in the closed-loop systems remain bounded. Lastly, the effectiveness of the algorithm is demonstrated through a numerical example.