Resilient Nash Equilibrium Seeking for Graphic Game Subject to Stochastic Deception Attacks With Its Application to Spacecraft Systems

In this article, we address a discrete-time Nash equilibrium seeking problem for a class of graphical game, which is susceptible to disturbances and stochastic deception attacks. To mitigate these unwanted factors, we devise a dynamic outlier-resistant extended state observer (ESO) for each player to estimate disturbances in the presence of anomalous measurement outputs. We rigorously establish the convergence of the outlier-resistant ESO. Moreover, we propose a distributed state estimation approach for each player to estimate real-time states of all players accounting for potential deception attacks during transmission. Following the compensation of disturbances based on these estimates, we formulate a Nash equilibrium (NE) seeking strategy aiming to achieve solutions where the upper bound of deviation from the unique equilibrium point of the nominal system is analytically derived ensuring a certain level of robustness denoted by $\epsilon$-NE solution. To assess the efficacy of the proposed game strategy, we introduce a spacecraft formation system and present comparative results. Additionally, we conduct a practical experiment using a wheeled mobile robot platform to demonstrate the applicability and effectiveness of our proposed methodology.