Event-Triggered Mechanism-Based Discrete-Time Nash Equilibrium Seeking for Graphic Game With Outlier-Resistant ESO

In this article, we consider a discrete-time Nash equilibrium (NE) seeking problem for graphic game subject to disturbances. For the first-order dynamics, the discrete-time outlier-resistant extended state observer (ESO)-based game strategy is proposed to enable the players to estimate the disturbances under effect of anomaly measurements and then compensate them. An event-triggered mechanism is applied between adjacent players to reduce the frequency of communication. The convergence of the outlier-resistant ESO and control strategy is presented. Moreover, the upper bound of <inline-formula> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula>-NE solution deviating from the unique point of nominal system is given analytically. Then, the addressed issues are extended to high-order game systems. The NE seeking-based control strategy for each player is designed such that the equilibrium point converges to the <inline-formula> <tex-math notation="LaTeX">$\epsilon$</tex-math> </inline-formula>-NE which is also analytically calculated. Finally, in order to verify the effectiveness of the proposed game strategy, an example of satellite system is given.