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A novel adaptive predefined-time sliding mode control scheme for synchronizing fractional order chaotic systems

Author

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  • Sun, Yunkang
  • Chen, Yuquan
  • Wang, Bing
  • Ma, Cheng

Abstract

In this paper, a novel adaptive predefined-time sliding model control scheme is presented for synchronizing fractional order chaotic systems subject to model uncertainties and external disturbances. A new sufficient criterion for predefined-time stability is proposed and proven to be valid by using the zero distribution property of sine functions. Based on the proposed criterion, a novel adaptive fractional order predefined-time sliding mode surface is designed and it is rigorously proven that the error states could converge to zero within a predefined time. Finally, a novel adaptive fractional order controller is proposed to ensure that the designed sliding mode surface can be reached within a predefined time. Numerous simulation results demonstrate that compared with the existing fixed-time control scheme, the proposed control scheme has the advantage of a simpler structure, fewer parameters and stronger robustness to the variation of initial values.

Suggested Citation

  • Sun, Yunkang & Chen, Yuquan & Wang, Bing & Ma, Cheng, 2024. "A novel adaptive predefined-time sliding mode control scheme for synchronizing fractional order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011627
    DOI: 10.1016/j.chaos.2024.115610
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    References listed on IDEAS

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    1. Runzi Luo & Haipeng Su, 2018. "The Robust Control and Synchronization of a Class of Fractional-Order Chaotic Systems with External Disturbances via a Single Output," Complexity, Hindawi, vol. 2018, pages 1-8, November.
    2. Shen, Zhiping & Li, Juntao, 2017. "Chaos control for a unified chaotic system using output feedback controllers," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 132(C), pages 208-219.
    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. 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).
    5. Zhang, Mengjiao & Zang, Hongyan & Bai, Luyuan, 2022. "A new predefined-time sliding mode control scheme for synchronizing chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    6. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
    7. Dehui Liu & Tianzeng Li & Yu Wang, 2022. "Adaptive Dual Synchronization of Fractional-Order Chaotic System with Uncertain Parameters," Mathematics, MDPI, vol. 10(3), pages 1-16, January.
    8. Agrawal, S.K. & Srivastava, M. & Das, S., 2012. "Synchronization of fractional order chaotic systems using active control method," Chaos, Solitons & Fractals, Elsevier, vol. 45(6), pages 737-752.
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