ABSTRACT This article investigates the distributed Nash equilibrium (NE) seeking problem in nonlinear multi‐agent systems subject to disturbances and switching communication topologies. To compensate for disturbances and unknown nonlinear components, an observer integrating the techniques of a high‐gain observer, extended state observer, and fixed‐time convergence is designed. Compared with observers exhibiting asymptotic or exponential convergence, the proposed fixed‐time observer ensures faster estimation, which can also accelerate the convergence of the NE‐seeking algorithm. Moreover, the nonlinear components in this article are modeled to represent both the nonlinear dynamics of individual players and the nonlinear couplings within the multi‐agent system, thereby broadening the applicability of the observer. With the observer's compensation, the NE‐seeking algorithm is designed based on the consensus protocol and gradient play, enabling the multi‐agent system to approximate the NE of a noncooperative game under partial decision information and switching topologies. By modeling the communication topology as a set of interchangeable undirected connected graphs, scenarios involving switching communication topologies can be handled. The effectiveness of the proposed algorithm is demonstrated by numerical simulations.
Niu et al. (Tue,) studied this question.