Distributed Nash Equilibrium Seeking for Nonlinear Players With Input Delay

This paper studies the distributed Nash equilibrium seeking problem for players subject to unknown nonlinear dynamics and input delay. By designing a distributed estimator for each player to estimate other players' decisions and embedding an auxiliary variable to compensate for the influence of unknown nonlinearities, the distributed Nash equilibrium seeking algorithms are obtained for first-, second-, and high-order nonlinear players, respectively. With the help of the Lyapunov stability theory and Lyapunov-Krasovskii functional approach, the maximum allowable input delay is determined and the global asymptotic convergence of players' decisions to the Nash equilibrium is proved. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed methods.