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Fuzzy-Based Tracking Control for a Class of Fractional-Order Systems with Time Delays

Author

Listed:
  • Jiae Yang

    (Research Institute of Intelligent Control and Systems, School of Astronautics, Harbin Institute of Technology, Harbin 150080, China)

  • Yujia Wang

    (Research Institute of Intelligent Control and Systems, School of Astronautics, Harbin Institute of Technology, Harbin 150080, China)

  • Tong Wang

    (Research Institute of Intelligent Control and Systems, School of Astronautics, Harbin Institute of Technology, Harbin 150080, China)

  • Xuebo Yang

    (Research Institute of Intelligent Control and Systems, School of Astronautics, Harbin Institute of Technology, Harbin 150080, China)

Abstract

This paper focuses on the tracking control problem for a family of fractional-order systems with unknown drift functions and unknown time delays. By employing fuzzy logic systems (FLSs), the unknown functions are approximated and compensated. Meanwhile, with the help of a hyperbolic tangent function and a sign function, the adverse effects of time-varying delays and FLSs approximation error are mitigated simultaneously. It should be stressed that the proposed method eliminates the assumption that the time delay is bounded by a known function. The stability analysis shows that the tracking error can converge to a small neighborhood of the origin. Finally, simulation is conducted to confirm the effectiveness of the presented control strategy.

Suggested Citation

  • Jiae Yang & Yujia Wang & Tong Wang & Xuebo Yang, 2022. "Fuzzy-Based Tracking Control for a Class of Fractional-Order Systems with Time Delays," Mathematics, MDPI, vol. 10(11), pages 1-22, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1884-:d:828690
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    References listed on IDEAS

    as
    1. Junzhang Qian & Ai Xiong & Wenli Ma, 2016. "Extended State Observer-Based Sliding Mode Control with New Reaching Law for PMSM Speed Control," Mathematical Problems in Engineering, Hindawi, vol. 2016, pages 1-10, June.
    2. Fei Qi & Yi Chai & Liping Chen & José A. Tenreiro Machado, 2020. "Delay-Dependent and Order-Dependent Guaranteed Cost Control for Uncertain Fractional-Order Delayed Linear Systems," Mathematics, MDPI, vol. 9(1), pages 1-13, December.
    3. Dumitru Baleanu & Vladimir E. Fedorov & Dmitriy M. Gordievskikh & Kenan Taş, 2019. "Approximate Controllability of Infinite-Dimensional Degenerate Fractional Order Systems in the Sectorial Case," Mathematics, MDPI, vol. 7(8), pages 1-15, August.
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