A RISE-based Distributed Robust Nash Equilibrium Seeking Strategy for Networked Games

This paper aims to accommodate games in which the players' dynamics are subject to un-modeled and disturbance terms. The un-modeled and disturbance terms are regarded as extended states for which an observer is designed to estimate them. More specifically, we adapt the idea from the Robust Integral of the Sign of the Error (RISE) method to achieve asymptotic observation of the extended states. Compensating the players' dynamics with the observed values, the control laws are designed to achieve the robust seeking of the Nash equilibrium for networked games. Through Lyapunov stability analysis, the convergence results are analytically investigated. Finally, the effectiveness of the proposed method is verified via conducting numerical simulations.