Distributed adaptive Nash equilibrium seeking and disturbance rejection for noncooperative games of high-order nonlinear systems with input saturation and input delay

This article aims to investigate Nash equilibrium seeking problems for noncooperative games played by high-order nonlinear multiagent systems subject to input saturation, input delay, and external disturbances. Based on the gradient play technique, an adaptive Nash equilibrium seeking algorithm is designed in a distributed fashion via backstepping, where a fixed-time sliding mode observer is used to tackle the problem of "explosion of terms." In the proposed algorithm, an extended-state observer and an adaptive distributed observer are included for state/disturbance estimates and information sharing, respectively. Detailed convergence results are presented by leveraging Lyapunov stability theory. Finally, the effectiveness of the proposed approach is numerically verified through simulation results.