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Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity

Author

Listed:
  • Chih-Hsueh Lin

    (Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan)

  • Guo-Hsin Hu

    (Department of Electronic Engineering, National Kaohsiung University of Science and Technology, Kaohsiung 80778, Taiwan
    Department of Industrial Upgrading Service, Metal Industries Research & Development Centre, Kaohsiung 81160, Taiwan)

  • Jun-Juh Yan

    (Department of Electronic Engineering, National Chin-Yi University of Technology, Taichung 41107, Taiwan)

Abstract

In this paper, a robust control design of chaos suppression is considered for generalized four-dimensional (4D) Lorenz–Stenflo systems subjected to matched/mismatched uncertainties and input nonlinearity. It is implemented by using rippling sliding mode control (SMC). A proportional-integral (PI) type scalar switching surface is designed such that the controlled dynamics in the sliding manifold becomes easy to analyze. Furthermore, only by using single rippling SMC even with input nonlinearity can we ensure the existence of the sliding mode for the controlled dynamics and suppress the chaotic behavior in a manner of rippling. Under the proposed control scheme, the chaos behavior in uncertain generalized 4D Lorenz–Stenflo systems subjected to mismatched uncertainties can be robustly suppressed to predictable bounds, which is not addressed in the literature. The numerical simulation results including matched/mismatched uncertainties and nonlinear inputs are presented to verify the robustness and validity of the rippling sliding mode controller.

Suggested Citation

  • Chih-Hsueh Lin & Guo-Hsin Hu & Jun-Juh Yan, 2020. "Chaos Suppression in Uncertain Generalized Lorenz–Stenflo Systems via a Single Rippling Controller with Input Nonlinearity," Mathematics, MDPI, vol. 8(3), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:327-:d:327550
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    References listed on IDEAS

    as
    1. Fuchen Zhang & Min Xiao, 2019. "Complex Dynamical Behaviors of Lorenz-Stenflo Equations," Mathematics, MDPI, vol. 7(6), pages 1-9, June.
    2. Fuchen Zhang & Rui Chen & Xiusu Chen, 2017. "Analysis of a Generalized Lorenz–Stenflo Equation," Complexity, Hindawi, vol. 2017, pages 1-6, December.
    3. Yin Li & Yulin Zhao & Zheng-an Yao, 2013. "Chaotic Control and Generalized Synchronization for a Hyperchaotic Lorenz-Stenflo System," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-18, December.
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    Cited by:

    1. Chih-Hsueh Lin & Chia-Wei Ho & Guo-Hsin Hu & Baswanth Sreeramaneni & Jun-Juh Yan, 2021. "Secure Data Transmission Based on Adaptive Chattering-Free Sliding Mode Synchronization of Unified Chaotic Systems," Mathematics, MDPI, vol. 9(21), pages 1-11, October.

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