Distributed Fuzzy Adaptive Nash Equilibrium Control for Nonlinear MASs Under Unreliable Communication Networks

This paper investigates the distributed fuzzy adaptive Nash equilibrium (NE) seeking problem in noncooperative games for nonlinear multi-agent systems under unreliable communication networks. Since the considered unreliable communication networks are jointly strongly connected switching networks and suffer from time-delays, agents cannot receive their neighboring agents' actions or can only obtain delayed actions. To estimate the neighboring agents' actions, a distributed NE seeking observer is developed. Then, based on the proposed distributed NE seeking observer and backstepping control technology, a distributed fuzzy adaptive control scheme is constructed by utilizing fuzzy logic systems and adopting integrable functions and bounded parameter estimation algorithms. It is proven that the observation error of the distributed NE seeking observer asymptotically converges to zero, and the developed fuzzy adaptive control scheme can ensure that the agents' outputs asymptotically converge to the NE of the noncooperative game. Moreover, the non-differentiable problem of virtual controllers is avoided. Finally, we apply the distributed fuzzy adaptive control scheme to marine surface vehicles, and the simulation and comparison results confirm its effectiveness.