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    Area of Science:

    • Control Theory
    • Game Theory
    • Machine Learning

    Background:

    • Addressing challenges in controlling unknown continuous-time linear systems within two-player zero-sum games.
    • Dealing with matched uncertainties dependent on system outputs and unknown exosystem states.

    Purpose of the Study:

    • To propose an online robust adaptive dynamic programming algorithm for unknown linear systems in continuous-time two-player zero-sum games.
    • To develop a single-iteration policy iteration (PI) scheme for online control.
    • To provide a rigorous convergence proof for the PI scheme.

    Main Methods:

    • Development of an online robust adaptive dynamic programming algorithm.
    • Utilizing a policy iteration (PI) scheme with a single iteration loop.
    • Introduction of a novel analytical method for PI convergence analysis.

    Main Results:

    • Guaranteed globally asymptotic stability of the closed-loop system.
    • Demonstration of the suboptimal property of the control system.
    • Validation of the proposed method's effectiveness through simulation studies.

    Conclusions:

    • The proposed online algorithm effectively controls unknown linear systems in zero-sum games.
    • The analytical method ensures convergence and stability guarantees.
    • The approach is suitable for systems with unknown dynamics and exosystems.