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Fixed-time control of a class of fractional-order chaotic systems via backstepping method

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  • Luo, Runzi
  • Liu, Shuai
  • Song, Zijun
  • Zhang, Fang

Abstract

This paper investigates the fixed-time control of a class of fractional-order systems via the backstepping method. A new fractional-order fixed-time stability theorem, which is a generalization of the integer order stability theorem, is presented. By using the proposed stability theorem, the fixed-time control problem of a class of fractional-order chaotic systems is investigated. Some fixed-time convergence criteria which have some pretty properties such as no singularity and no chattering are presented via backstepping method. Simulation results are given to show the effectiveness of the presented results.

Suggested Citation

  • Luo, Runzi & Liu, Shuai & Song, Zijun & Zhang, Fang, 2023. "Fixed-time control of a class of fractional-order chaotic systems via backstepping method," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:chsofr:v:167:y:2023:i:c:s0960077922012553
    DOI: 10.1016/j.chaos.2022.113076
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    References listed on IDEAS

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    1. Dutta, Maitreyee & Roy, Binoy Krishna, 2021. "A new memductance-based fractional-order chaotic system and its fixed-time synchronisation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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    3. Shirkavand, Mehrdad & Pourgholi, Mahdi & Yazdizadeh, Alireza, 2022. "Robust global fixed-time synchronization of different dimensions fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    4. Huang, Sunhua & Zhou, Bin & Bu, Siqi & Li, Canbing & Zhang, Cong & Wang, Huaizhi & Wang, Tao, 2019. "Robust fixed-time sliding mode control for fractional-order nonlinear hydro-turbine governing system," Renewable Energy, Elsevier, vol. 139(C), pages 447-458.
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    Cited by:

    1. Hou, Yi-You & Lin, Ming-Hung & Saberi-Nik, Hassan & Arya, Yogendra, 2024. "Boundary analysis and energy feedback control of fractional-order extended Malkus–Robbins dynamo system," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    2. Bekiros, Stelios & Yao, Qijia & Mou, Jun & Alkhateeb, Abdulhameed F. & Jahanshahi, Hadi, 2023. "Adaptive fixed-time robust control for function projective synchronization of hyperchaotic economic systems with external perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).

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