Distributed Nash Equilibrium Seeking for Nonlinear Players With Time-Varying Measurement Delays

This article investigates the distributed Nash equilibrium seeking problem for the players with unknown nonlinearities and time-varying measurement delays, where the small delays and the large delays are allowed to occur in an alternating manner. A new predictor independent of the unknown nonlinearities is designed to overcome the difficulties brought by the time-varying measurement delays. Then, the distributed estimator and the auxiliary variable are developed for each player to estimate other players' actions and compensate for the unknown nonlinearities, respectively. After constructing a novel Lyapunov-Krasovskii functional, it is proved that the actions of all players globally asymptotically converge to the Nash equilibrium. Finally, simulation examples are given to demonstrate the effectiveness of the proposed approaches.