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    This study introduces a novel outlier-resistant extended state observer (ESO)-based strategy for discrete-time Nash equilibrium (NE) seeking in graphic games, enhancing disturbance estimation and compensation for robust control.

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    Area of Science:

    • Control Systems Engineering
    • Game Theory
    • Distributed Systems

    Background:

    • Graphic games are susceptible to disturbances and anomaly measurements.
    • Existing Nash equilibrium (NE) seeking methods may lack robustness against such uncertainties.
    • Efficient communication strategies are needed in distributed game systems.

    Purpose of the Study:

    • To develop a disturbance-resilient discrete-time Nash equilibrium (NE) seeking strategy for graphic games.
    • To enhance control system robustness using an outlier-resistant extended state observer (ESO).
    • To reduce communication load via an event-triggered mechanism.

    Main Methods:

    • A discrete-time outlier-resistant extended state observer (ESO)-based control strategy is proposed.
    • An event-triggered communication mechanism is implemented between adjacent players.
    • Convergence analysis for the ESO and control strategy is provided, including analytical bounds for the epsilon-Nash equilibrium (ϵ-NE).

    Main Results:

    • The proposed strategy effectively estimates and compensates for disturbances under anomaly measurements.
    • The outlier-resistant ESO and control strategy demonstrate convergence.
    • Analytical upper bounds for the ϵ-NE solution deviation from the nominal system's unique point are derived.
    • The approach is successfully extended to high-order game systems.

    Conclusions:

    • The developed game strategy ensures convergence to an ϵ-NE for both first-order and high-order graphic games.
    • The event-triggered mechanism enhances communication efficiency.
    • The strategy's effectiveness is validated through a satellite system example.