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Stability and Admissibility Analysis for Zero-Sum Games Under General Value Iteration Formulation.

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    This study introduces a new criterion for the general value iteration (GVI) algorithm in zero-sum games, ensuring policy pair admissibility and system stability. An improved GVI algorithm guarantees stable control for evolving policy pairs.

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    Area of Science:

    • Control Theory
    • Game Theory
    • Reinforcement Learning

    Background:

    • The general value iteration (GVI) algorithm is crucial for solving discrete-time zero-sum games.
    • Assessing the stability and admissibility of iterative policies is essential for reliable control system design.

    Purpose of the Study:

    • To investigate the stability and admissibility properties of the GVI algorithm for discrete-time zero-sum games.
    • To develop an improved GVI algorithm with guaranteed admissibility and stability.
    • To demonstrate the application of theoretical results to linear and nonlinear systems.

    Main Methods:

    • Theoretical analysis of stability and admissibility properties.
    • Development of a new admissibility criterion for policy pairs.
    • Design of an improved GVI algorithm based on the new criterion.
    • Demonstration of state trajectory confinement within an attraction domain.

    Main Results:

    • A novel criterion for determining the admissibility of policy pairs in GVI is established.
    • An improved GVI algorithm is proposed, guaranteeing admissible policy pairs if the criterion is met.
    • The state trajectory remains within the attraction domain for both fixed and evolving policy pairs.
    • Evolving policy pairs are shown to effectively stabilize controlled systems.

    Conclusions:

    • The developed admissibility criterion and improved GVI algorithm enhance the reliability of control systems in zero-sum games.
    • The findings are applicable to both linear and nonlinear systems, utilizing offline and online critic control design.
    • The research contributes to robust control strategies through theoretical advancements in value iteration algorithms.