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Quadratic Tracking Control of Linear Stochastic Systems with Unknown Dynamics Using Average Off-Policy Q-Learning Method

Author

Listed:
  • Longyan Hao

    (Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
    These authors contributed equally to this work.)

  • Chaoli Wang

    (Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
    These authors contributed equally to this work.)

  • Yibo Shi

    (Department of Control Science and Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China)

Abstract

This article investigates the optimal tracking control problem for data-based stochastic discrete-time linear systems. An average off-policy Q-learning algorithm is proposed to solve the optimal control problem with random disturbances. Compared with the existing off-policy reinforcement learning (RL) algorithm, the proposed average off-policy Q-learning algorithm avoids the assumption of an initial stability control. First, a pole placement strategy is used to design an initial stable control for systems with unknown dynamics. Second, the initial stable control is used to design a data-based average off-policy Q-learning algorithm. Then, this algorithm is used to solve the stochastic linear quadratic tracking (LQT) problem, and a convergence proof of the algorithm is provided. Finally, numerical examples show that this algorithm outperforms other algorithms in a simulation.

Suggested Citation

  • Longyan Hao & Chaoli Wang & Yibo Shi, 2024. "Quadratic Tracking Control of Linear Stochastic Systems with Unknown Dynamics Using Average Off-Policy Q-Learning Method," Mathematics, MDPI, vol. 12(10), pages 1-21, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1533-:d:1394587
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