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

Jiae Yang, Yujia Wang, Tong Wang and Xuebo Yang
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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

Mathematics, 2022, vol. 10, issue 11, 1-22

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.

Keywords: fractional-order systems; fuzzy logic systems; time delays; unknown nonlinear functions; hyperbolic tangent function (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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