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Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances

Author

Listed:
  • Amir Rezaie

    (Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan 45371-38791, Iran)

  • Saleh Mobayen

    (Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, Zanjan 45371-38791, Iran
    Graduate School of Intelligent Data Science, National Yunlin University of Science and Technology, Douliou 64002, Yunlin, Taiwan)

  • Mohammad Reza Ghaemi

    (Department of Mathematics, Faculty of Sciences, University of Zanjan, Zanjan 45371-38791, Iran)

  • Afef Fekih

    (Department of Electrical and Computer Engineering, University of Louisiana at Lafayette, Lafayette, LA 70504, USA)

  • Anton Zhilenkov

    (Department of Cyber-Physical Systems, St. Petersburg State Marine Technical University, 190121 Saint-Petersburg, Russia)

Abstract

This paper addresses the fixed-time stability problem of chaotic systems with internal uncertainties and external disturbances. To this end, new sliding-mode surfaces are introduced to design fixed-time controllers for the stabilization of perturbed chaotic systems. First, the required conditions for deriving fixed-time stability are determined. Then, using the obtained stability theorems and sliding mode techniques, the controllers are synthesized. The proposed controller enables the convergence of the trajectories of the chaotic system to the origin in finite time, independently of the initial conditions. The performance of the proposed approach is assessed using a simulation study of a PMSM system and the Matouk system. Among the advantages of the proposed controller are its robustness to external disturbances and the boundedness of the settling time to a constant value for any initial condition.

Suggested Citation

  • Amir Rezaie & Saleh Mobayen & Mohammad Reza Ghaemi & Afef Fekih & Anton Zhilenkov, 2023. "Design of a Fixed-Time Stabilizer for Uncertain Chaotic Systems Subject to External Disturbances," Mathematics, MDPI, vol. 11(15), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:15:p:3273-:d:1202392
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    References listed on IDEAS

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    1. Zhoubin Sheng & Chunbiao Li & Yikai Gao & Zhinan Li & Lin Chai, 2023. "A Switchable Chaotic Oscillator with Multiscale Amplitude/Frequency Control," Mathematics, MDPI, vol. 11(3), pages 1-11, January.
    2. Runzi Luo & Meichun Huang & Haipeng Su, 2019. "Robust Control and Synchronization of 3-D Uncertain Fractional-Order Chaotic Systems with External Disturbances via Adding One Power Integrator Control," Complexity, Hindawi, vol. 2019, pages 1-11, May.
    3. Zizhao Xie & Jingru Sun & Yiping Tang & Xin Tang & Oluyomi Simpson & Yichuang Sun, 2023. "A K-SVD Based Compressive Sensing Method for Visual Chaotic Image Encryption," Mathematics, MDPI, vol. 11(7), pages 1-20, March.
    4. Luo, Danfeng & Tian, Mengquan & Zhu, Quanxin, 2022. "Some results on finite-time stability of stochastic fractional-order delay differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
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    Cited by:

    1. Shichao Jia & Cheng Hu & Haijun Jiang, 2024. "Fixed/Preassigned-Time Synchronization of Fuzzy Memristive Fully Quaternion-Valued Neural Networks Based on Event-Triggered Control," Mathematics, MDPI, vol. 12(9), pages 1-31, April.
    2. Shichao Jia & Cheng Hu & Haijun Jiang, 2023. "Fixed/Preassigned-Time Synchronization of Fully Quaternion-Valued Cohen–Grossberg Neural Networks with Generalized Time Delay," Mathematics, MDPI, vol. 11(23), pages 1-20, November.

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