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Observer-based Adaptive Fuzzy Control for Nonlinear Fractional-Order Systems via Backstepping and Sliding Mode Techniques

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Abstract

Compared with integral-order calculus, fractional calculus is better at depicting the real process with memory property and history-dependent property. As a result, this work investigates a class of nonlinear strict-feedback fractional-order systems and presents a novel control strategy. To begin, in order to cope with the unknown drift functions and unmeasurable system states, fuzzy logic systems (FLSs)and a robust fractional-order state observer are designed. Second, in order to further reduce the FLS approximation error and state estimation error, a hyperbolic tangent function is implemented. Third, the problem of the differential explosion caused by repeated differentiation when employing the backstepping technique when designing a control scheme is also overcome without the help of a command filter or dynamic surface control. Finally, theoretical analysis and simulation results show that by combining the backstepping procedure with the sliding mode technique, not only is it possible to achieve strong robustness against unknown drift function and unknown external time-varying disturbance, but also that the tracking error can converge to the vicinity of the origin.

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Funding

This work was supported by the National Natural Science Foundation of China under Grant 61803122 and Grant 61773143, in part by the 111 Project under Grant B16014, in part by the Special Project of Heilongjiang Postdoctoral Science Foundation under Grant LBH-TZ2011, in part by special projects in key fields of Guangdong Provincial Department of Education of China under Grant 2019KZDZX1025, in part by the funding AC01202101103 from Shenzhen Institute of Artificial Intelligence and Robotics for Society, and in part by Shenzhen Peacock Plan of Shenzhen Science and Technology Program (Grant No.KQTD2016113010470345).

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Authors and Affiliations

  1. Research Institute of Intelligent Control and Systems, Harbin Institute of Technology, Harbin, 150080, China

    Jiae Yang, Yujia Wang, Tong Wang, Xuebo Yang & Yu Liu

  2. College of Science, Liaoning University of Technology, Jinzhou, 121001, China

    Shuai Sui

  3. School of Intelligent Manufacturing, Wuyi University, Jiangmen, 529020, China

    Fuqin Deng

  4. Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, 518000, China

    Fuqin Deng

  5. 3irobotix, Shenzhen, 518000, China

    Fuqin Deng

Authors
  1. Jiae Yang
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  2. Yujia Wang
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  3. Fuqin Deng
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  4. Tong Wang
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  5. Shuai Sui
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  6. Xuebo Yang
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  7. Yu Liu
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Corresponding authors

Correspondence to Yujia Wang, Fuqin Deng or Xuebo Yang.

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Yang, J., Wang, Y., Deng, F. et al. Observer-based Adaptive Fuzzy Control for Nonlinear Fractional-Order Systems via Backstepping and Sliding Mode Techniques. Int. J. Fuzzy Syst. 24, 3650–3665 (2022). https://doi.org/10.1007/s40815-022-01353-5

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  • DOI: https://doi.org/10.1007/s40815-022-01353-5

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