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    This study presents a novel projection-based pseudo-gradient method for distributed generalized Nash equilibrium (GNE) seeking in N-player games with linear dynamics and switching networks. The algorithm ensures convergence and satisfies inequality constraints for applications like DFIGs.

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    Area of Science:

    • Control Systems Engineering
    • Game Theory
    • Networked Systems

    Background:

    • Distributed generalized Nash equilibrium (GNE) seeking is crucial for multi-agent systems.
    • Existing methods face challenges with switching networks and inequality constraints.
    • Linear dynamics in N-player games add complexity to GNE seeking.

    Purpose of the Study:

    • To develop a robust distributed algorithm for GNE seeking in N-player games.
    • To address challenges posed by jointly strongly connected switching networks.
    • To incorporate inequality constraints within the GNE seeking framework.

    Main Methods:

    • A projection-based pseudo-gradient method is proposed.
    • The algorithm is designed for linear dynamics over switching networks.
    • Convergence analysis utilizes the generalized Barbalat's lemma.

    Main Results:

    • The proposed method ensures convergence under jointly strongly connected switching networks.
    • The algorithm successfully handles individual and shared inequality constraints.
    • Simulation results validate the algorithm's effectiveness for DFIGs.

    Conclusions:

    • The developed algorithm effectively achieves distributed GNE seeking.
    • The approach is applicable to complex systems with dynamic constraints.
    • This work contributes to the advancement of distributed optimization and control.