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

• Published in: IEEE transactions on industrial electronics (1982) pp. 1 - 10
• Main Authors: Yuan, Huanhuan, Yuan, Yuan, Xia, Yuanqing
• Format: Journal Article
• Language: English
• Published: IEEE 20.03.2025
• Subjects: Convergence; Cost function; Games; Graph game; Graphics; Nash equilibrium; Nash equilibrium (NE) seeking; outlier-resistant extended state observer (ESO); Space vehicles; stochastic deception attack; Sufficient conditions; Uncertainty; Vectors; Vehicle dynamics
• ISSN: 0278-0046; 1557-9948
• DOI: 10.1109/TIE.2025.3549096

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 ε-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.