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    Area of Science:

    • Control Theory
    • Game Theory
    • Distributed Systems

    Background:

    • Monotone games are crucial in economics and engineering.
    • Distributed Nash equilibrium seeking is challenging due to disturbances and lack of strong monotonicity.
    • Existing methods often struggle with unknown disturbance bounds and prescribed-time convergence.

    Purpose of the Study:

    • To develop prescribed-time distributed robust Nash equilibrium seeking algorithms for monotone games.
    • To address unknown and time-varying disturbances.
    • To guarantee convergence to the least-norm Nash equilibrium.

    Main Methods:

    • Introduced a regularization term with a prescribed-time decaying parameter.
    • Developed a signum-based distributed algorithm using integral sliding mode, leader-following consensus, and gradient methods.
    • Devised an adaptive integral sliding mode strategy to handle unknown disturbance bounds.

    Main Results:

    • Sufficient conditions derived for convergence to the least-norm Nash equilibrium in a prescribed time.
    • Algorithms demonstrated robustness against unknown and time-varying disturbances.
    • Numerical simulations validated the effectiveness for formation control.

    Conclusions:

    • The proposed strategies effectively achieve prescribed-time distributed robust Nash equilibrium seeking for monotone games.
    • The methods are applicable to scenarios with unknown disturbances and bounded uncertainties.
    • The research contributes to advancing distributed optimization and control under uncertainty.