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Q-Learning Approach to Finite-Horizon H∞ Tracking With Partial Observation.

Mingxiang Liu, Qianqian Cai, Wei Meng

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    This study introduces novel model-free reinforcement learning algorithms for discrete-time systems with partial observations. These data-driven methods address finite-horizon H-infinity tracking control challenges without needing an initial policy or discount factor.

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    Area of Science:

    • Control Theory
    • Reinforcement Learning
    • Game Theory

    Background:

    • Existing reinforcement learning (RL) methods often require full state information and are limited to infinite-horizon, time-invariant systems.
    • Finite-horizon control with partial observations and unknown dynamics presents significant challenges, including the need for time-varying Riccati equations.
    • Model-free approaches are desirable for systems where dynamics are unknown, relying solely on input-output data.

    Purpose of the Study:

    • To investigate the finite-horizon H-infinity tracking control problem for discrete-time linear systems with partial observations and unknown dynamics.
    • To develop model-free reinforcement learning algorithms that overcome limitations of existing approaches, particularly regarding state information and system horizon.
    • To provide a framework for solving time-varying control problems without requiring an initially admissible policy or discount factor.

    Main Methods:

    • Reconstruction of system state from historical input-output trajectories to create a data-driven system representation.
    • Definition of a time-varying Q-function based on input-output data.
    • Proposal of two minimax Q-learning algorithms designed for model-free, data-driven control.

    Main Results:

    • The developed algorithms successfully reconstruct system states and define input-output-based Q-functions.
    • The minimax Q-learning algorithms do not require an initially admissible policy and avoid discount factors, enhancing stability guarantees.
    • The framework demonstrates extensibility to both infinite-horizon and time-varying systems without structural changes.

    Conclusions:

    • The proposed data-driven, model-free reinforcement learning algorithms effectively address the finite-horizon H-infinity tracking control problem for discrete-time systems with partial observations.
    • Theoretical convergence is proven, and simulation results validate the algorithms' effectiveness.
    • This work offers a significant advancement in reinforcement learning for control, particularly for systems with unknown dynamics and partial state information.