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A Fully Data-Driven Value Iteration for Stochastic LQR: Convergence, Robustness, and Stability.

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    Data-driven control using value iteration (VI) ensures stability and convergence for unknown systems, even with noise. A novel adaptive dynamic programming algorithm offers robust control without initial policy knowledge.

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    Area of Science:

    • Control Theory
    • Machine Learning
    • Data-Driven Systems

    Background:

    • Traditional model-based reinforcement learning (RL) relies on system parameter estimation.
    • Nonmodel-based data-driven control learns policies directly from data, offering adaptability but facing challenges with noise and disturbances.
    • Existing methods often require restrictive assumptions on initial value functions or prior knowledge of admissible control policies.

    Purpose of the Study:

    • To establish the convergence, robustness, and stability of value iteration (VI) for data-driven control of stochastic linear quadratic (LQ) systems with unknown dynamics.
    • To develop a novel nonmodel-based robust adaptive dynamic programming (ADP) algorithm for adaptive optimal controller design.
    • To demonstrate the practical applicability of the proposed methods in noisy environments and beyond traditional control tasks.

    Main Methods:

    • Proving global exponential stability of VI for noise-free stochastic LQ systems with relaxed initial value matrix assumptions.
    • Extending the analysis to include external disturbances, demonstrating input-to-state stability (ISS) and convergence within a small neighborhood of the optimal solution.
    • Developing a new nonmodel-based robust adaptive dynamic programming (ADP) algorithm that does not require prior knowledge of an initial admissible control policy.

    Main Results:

    • Value iteration (VI) is proven to be globally exponentially stable for noise-free settings, removing restrictive initial value function assumptions.
    • VI demonstrates small-disturbance input-to-state stability (ISS) and converges near the optimal solution in the presence of external disturbances.
    • The proposed robust adaptive dynamic programming (ADP) algorithm shows convergence and stability in numerical experiments, outperforming established methods in noisy conditions.

    Conclusions:

    • Data-driven control using VI provides a robust and stable framework for systems with unknown dynamics, even under noisy conditions.
    • The novel nonmodel-based ADP algorithm offers a practical solution for adaptive optimal control without requiring initial policy knowledge.
    • The methods are validated through applications in data center cooling and dynamic portfolio allocation, highlighting their broad relevance.