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Model-free finite-horizon optimal tracking control of discrete-time linear systems

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  • Wang, Wei
  • Xie, Xiangpeng
  • Feng, Changyang

Abstract

Conventionally, the finite-horizon linear quadratic tracking (FHLQT) problem relies on solving the time-varying Riccati equations and the time-varying non-causal difference equations as the system dynamics is known. In this paper, with unknown system dynamics being considered, a Q-function-based model-free method is developed to solve the FHLQT problem. First, an augmented system consisting of the controlled system and the desired trajectory system is formulated, and the FHLQT problem transforms to the finite-horizon linear quadratic regulator (FHLQR) problem with the augmented system. Then, a time-varying Q-function which depends explicitly on the control input is defined. With the defined time-varying Q-function, a model-free finite-horizon control method is developed to approximate the solutions of the time-varying Riccati equations of the transformed FHLQR problem. At last, simulation studies are carried out to verify the validity of the developed method.

Suggested Citation

  • Wang, Wei & Xie, Xiangpeng & Feng, Changyang, 2022. "Model-free finite-horizon optimal tracking control of discrete-time linear systems," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    • Handle: RePEc:eee:apmaco:v:433:y:2022:i:c:s009630032200474x
    DOI: 10.1016/j.amc.2022.127400
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    References listed on IDEAS

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    1. Qiao Lin & Qinglai Wei & Derong Liu, 2017. "A novel optimal tracking control scheme for a class of discrete-time nonlinear systems using generalised policy iteration adaptive dynamic programming algorithm," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(3), pages 525-534, February.
    2. Shizheng Wan & Xiaofei Chang & Quancheng Li & Jie Yan, 2019. "Finite-Horizon Optimal Tracking Guidance for Aircraft Based on Approximate Dynamic Programming," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-12, March.
    3. Cui, Lili & Xie, Xiangpeng & Wang, Xiaowei & Luo, Yanhong & Liu, Jingbo, 2019. "Event-triggered single-network ADP method for constrained optimal tracking control of continuous-time non-linear systems," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 220-234.
    4. Yoo, Sung Jin & Park, Bong Seok, 2021. "Quantized feedback control strategy for tracking performance guarantee of nonholonomic mobile robots with uncertain nonlinear dynamics," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    5. Wang, Di & Liu, Can & Ding, Dawei & Gao, Suixiang & Chu, Ming, 2022. "Finite-time optimal tracking control using augmented error system method," Applied Mathematics and Computation, Elsevier, vol. 424(C).
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