Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode

Iranian Journal of Science and Technology, Transactions of Electrical Engineering volume 43, pages339–347(2019)Cite this article

Abstract

This article presents a novel adaptive finite-time stabilization technique based on global sliding mode for disturbed chaotic flow with a single unstable node. The considered chaotic flow has unusual characteristics containing attractor merging, symmetry breaking, attracting tori and different forms of multi-stability. A nonlinear function is employed in the global sliding surface to modify damping ratio and improve the transient performance. The damping ratio of the closed-loop system is improved when the states converge to the origin. Using the new chattering-free controller, the reaching mode is removed and the sliding behavior is presented right from the first instant. The adaptive finite-time tuning law eliminates the requirement of the information about the disturbances’ bounds. Illustrative simulations are provided to display the efficiency of the proposed scheme.

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Acknowledgements

This work was partially supported by the Spanish Ministry of Economy, Industry and Competitiveness, under Grants DPI2016-77407-P (AEI/FEDER, UE) and DPI2015-64170-R (MINECO/FEDER).

Author information

Affiliations

  1. Department of Electrical Engineering, Faculty of Engineering, University of Zanjan, Zanjan, Iran

    Saleh Mobayen

  2. Department of Physics, Lanzhou University of Technology, Lanzhou, 730050, China

    Jun Ma

  3. Department of Mathematics, Universitat Politècnica de Catalunya-BarcelonaTech (ESEIAAT), Terrasa, Spain

    Gisela Pujol-Vazquez

  4. Department of Mathematics, Universitat Politècnica de Catalunya-BarcelonaTech (EEBE), Barcelona, Spain

    Leonardo Acho

  5. Department of Engineering Design and Mathematics, University of the West of England, Bristol, UK

    Quanmin Zhu

Authors
  1. Saleh Mobayen
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  2. Jun Ma
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  3. Gisela Pujol-Vazquez
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  4. Leonardo Acho
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  5. Quanmin Zhu
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Correspondence to Saleh Mobayen.

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Mobayen, S., Ma, J., Pujol-Vazquez, G. et al. Adaptive Finite-Time Stabilization of Chaotic Flow with a Single Unstable Node Using a Nonlinear Function-Based Global Sliding Mode. Iran J Sci Technol Trans Electr Eng 43, 339–347 (2019). https://doi.org/10.1007/s40998-018-0153-6

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Keywords

  • Global sliding mode
  • Adaptive gain tuning
  • Finite-time control
  • Chaotic flow
  • Unstable node