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Fixed Time Adaptive Fuzzy Dynamic Surface Control for Pure Feedback Stochastic Nonlinear Systems

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Abstract

In this paper, an adaptive fuzzy fixed time control strategy based on dynamic surface control (DSC) method is proposed for pure feedback stochastic nonlinear systems with external disturbances. The mean value theorem is introduced to transform the pure feedback structure to strict feedback structure in order to deal with the problem of nonaffine appearance of the considered systems. Then, combining backstepping method with fixed time stability theorem, an adaptive fuzzy fixed time controller is designed, where the DSC method and adaptive fuzzy technique are utilized to handle “explosion of complexity” resulting from backstepping method and approximate unknown nonlinear functions, respectively. Finally, we give simulation results based on the proposed control strategy and we can obtain that the considered systems are semiglobally uniform and ultimately bounded and the tracking errors are driven to a small neighborhood of the origin in a fixed time.

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Acknowledgements

This work was partially supported by National Natural Science Foundation of China under Grant (62201200), the Program for Science and Technology Innovation Talents in the University of Henan Province under Grant (23HASTIT021), the Key Scientific Research Projects of Universities in Henan Province (22A413002), the Scientific and Technological Project of Henan Province under Grant (222102210056, 222102240009), the Postdoctoral Research Grant in Henan Province under Grant (202003077), the Science and Technology Development Plan of Joint Research Program of Henan under Grant (222103810036).

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Authors and Affiliations

  1. School of Mechatronics Engineering, Henan University of Science and Technology, Luoyang, 471023, Henan, China

    Nan Wang

  2. Research Institute of Intelligent System Science, Longmen Laboratory, Luoyang, 471000, Henan, China

    Nan Wang, Fazhan Tao & Zhumu Fu

  3. College of Information Engineering, Henan University of Science and Technology, Luoyang, 471023, Henan, China

    Pengyu Fan, Fazhan Tao & Zhumu Fu

  4. Luoyang Normal University, Luoyang, 471934, Henan, China

    Mengyang Li

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  1. Nan Wang
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  2. Pengyu Fan
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Correspondence to Mengyang Li or Zhumu Fu.

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Wang, N., Fan, P., Li, M. et al. Fixed Time Adaptive Fuzzy Dynamic Surface Control for Pure Feedback Stochastic Nonlinear Systems. Int. J. Fuzzy Syst. 25, 2748–2759 (2023). https://doi.org/10.1007/s40815-023-01525-x

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  • DOI: https://doi.org/10.1007/s40815-023-01525-x

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