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The Adaptive Optimal Output Feedback Tracking Control of Unknown Discrete-Time Linear Systems Using a Multistep Q-Learning Approach

Author

Listed:
  • Xunde Dong

    (School of Automation Science and Engineering, South China University of Technology, Guangzhou 510641, China)

  • Yuxin Lin

    (School of Automation Science and Engineering, South China University of Technology, Guangzhou 510641, China)

  • Xudong Suo

    (Intelligent Mobile Robot Research Institute (Zhongshan), Zhongshan 528478, China)

  • Xihao Wang

    (School of Automation Science and Engineering, South China University of Technology, Guangzhou 510641, China)

  • Weijie Sun

    (School of Automation Science and Engineering, Key Laboratory of Autonomous Systems and Networked Control, Ministry of Education, Guangdong Engineering Technology Research Center of Unmanned Aerial Vehicle System, South China University of Technology, Guangzhou 510641, China)

Abstract

This paper investigates the output feedback (OPFB) tracking control problem for discrete-time linear (DTL) systems with unknown dynamics. To solve this problem, we use an augmented system approach, which first transforms the tracking control problem into a regulation problem with a discounted performance function. The solution to this problem is derived using a Bellman equation, based on the Q-function. In order to overcome the challenges of unmeasurable system state variables, we employ a multistep Q-learning algorithm that surpasses the advantages of the policy iteration (PI) and value iteration (VI) techniques and state reconstruction methods for output feedback control. As such, the requirement for an initial stabilizing control policy for the PI method is removed and the convergence speed of the learning algorithm is improved. Finally, we demonstrate the effectiveness of the proposed scheme using a simulation example.

Suggested Citation

  • Xunde Dong & Yuxin Lin & Xudong Suo & Xihao Wang & Weijie Sun, 2024. "The Adaptive Optimal Output Feedback Tracking Control of Unknown Discrete-Time Linear Systems Using a Multistep Q-Learning Approach," Mathematics, MDPI, vol. 12(4), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:509-:d:1334687
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    References listed on IDEAS

    as
    1. Rui Luo & Zhinan Peng & Jiangping Hu, 2023. "On Model Identification Based Optimal Control and It’s Applications to Multi-Agent Learning and Control," Mathematics, MDPI, vol. 11(4), pages 1-19, February.
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