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Amir Parviz Valadbeigi, Ali Khaki Sedigh, F L Lewis

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    This study establishes conditions for static output-feedback (OPFB) H∞ control in discrete-time systems, revealing the solution as a Nash equilibrium. A Q-learning algorithm finds this solution online using system data, bypassing the need for system matrices.

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    Area of Science:

    • Control Theory
    • Systems Engineering
    • Machine Learning

    Background:

    • The H∞ control problem addresses system stability and performance under uncertainty.
    • Static output-feedback (OPFB) control is desirable for its simplicity but challenging to design.
    • Existing methods often require full knowledge of system dynamics.

    Purpose of the Study:

    • To derive necessary and sufficient conditions for the existence of static output-feedback H∞ control solutions.
    • To demonstrate that the OPFB H∞ control solution corresponds to a Nash equilibrium.
    • To develop an online Q-learning algorithm for finding the H∞ OPFB solution without prior system knowledge.

    Main Methods:

    • Derivation of existence conditions for static output-feedback H∞ control.
    • Formulation of the H∞ control problem as a game-theoretic problem to establish Nash equilibrium.
    • Development of a Q-learning algorithm to solve the game algebraic Riccati equation online using measured data.

    Main Results:

    • Necessary and sufficient conditions for the static output-feedback H∞ control problem are established.
    • The static output-feedback H∞ control solution is proven to be a Nash equilibrium.
    • An effective online Q-learning algorithm is presented for H∞ OPFB control, demonstrated via simulation.

    Conclusions:

    • The study provides a theoretical framework and a practical algorithm for static output-feedback H∞ control.
    • The Q-learning approach offers an efficient, data-driven method for solving complex control problems online.
    • This work contributes to robust control design for linear discrete-time systems.