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Stochastic adaptive fixed-time stabilization of chaotic systems with applications in PMSM and FWS

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  • Wu, Jie
  • Xu, Wei
  • Wang, Xiaofeng
  • Ma, Ru-ru

Abstract

This investigation addresses the problem of fixed-time stabilization of the chaotic systems influenced by environmental noise. An adaptive control scheme is employed so that it is not necessary to set the related control gains in advance. Specifically, the adaptive control is integrated with fixed-time control protocol successfully for guaranteeing the stability of chaotic systems. In the light of stochastic fixed-time stability theory, the criteria are deduced to ensure the (fixed-time) stabilization of chaotic systems, and the upper bound time is estimated, which is irrelevant to the initial states of the systems. For validating the correctness and effectiveness of theoretical analysis, two representative application cases of permanent magnet synchronous motor (PMSM) and food web system (FWS) are selected at last.

Suggested Citation

  • Wu, Jie & Xu, Wei & Wang, Xiaofeng & Ma, Ru-ru, 2021. "Stochastic adaptive fixed-time stabilization of chaotic systems with applications in PMSM and FWS," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    • Handle: RePEc:eee:chsofr:v:153:y:2021:i:p2:s096007792100936x
    DOI: 10.1016/j.chaos.2021.111582
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    References listed on IDEAS

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    1. Yao, Qijia, 2021. "Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    2. Maoxing Liu & Jie Wu & Yong-zheng Sun, 2017. "Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control," Mathematical Problems in Engineering, Hindawi, vol. 2017, pages 1-11, December.
    3. Nian, Fuzhong & Liu, Xinmeng & Zhang, Yaqiong, 2018. "Sliding mode synchronization of fractional-order complex chaotic system with parametric and external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 22-28.
    4. Wang, Cong & Zhang, Hongli & Fan, Wenhui & Ma, Ping, 2018. "Adaptive control method for chaotic power systems based on finite-time stability theory and passivity-based control approach," Chaos, Solitons & Fractals, Elsevier, vol. 112(C), pages 159-167.
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    Cited by:

    1. Xue, Haibo & Liu, Xinghua, 2023. "A novel fast terminal sliding mode with predefined-time synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).

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