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Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays

Author

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  • Jun-Juh Yan

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

  • Hang-Hong Kuo

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

Abstract

In this paper, by adopting sliding mode control, an adaptive memoryless control scheme has been developed for uncertain Rössler chaotic systems with unknown time delays. Firstly, the proposed adaptive control can force the trajectories of controlled Rössler time-delayed chaotic systems into the specified sliding manifold. Then, the Riemann sum is introduced to analyze the stability of the equivalent dynamics in the sliding manifold. The control performance can be predicted even if the controlled systems have unmatched uncertainties and unknown time delays, which have not been well addressed in the literature. Numerical simulations are included to demonstrate the feasibility of the proposed scheme.

Suggested Citation

  • Jun-Juh Yan & Hang-Hong Kuo, 2022. "Adaptive Memoryless Sliding Mode Control of Uncertain Rössler Systems with Unknown Time Delays," Mathematics, MDPI, vol. 10(11), pages 1-13, May.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:11:p:1885-:d:828892
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    References listed on IDEAS

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    1. Hien, Le Van & Trinh, Hieu, 2016. "Exponential stability of time-delay systems via new weighted integral inequalities," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 335-344.
    2. Bukhari, Ayaz Hussain & Raja, Muhammad Asif Zahoor & Rafiq, Naila & Shoaib, Muhammad & Kiani, Adiqa Kausar & Shu, Chi-Min, 2022. "Design of intelligent computing networks for nonlinear chaotic fractional Rossler system," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    3. Zeng, Hong-Bing & Liu, Xiao-Gui & Wang, Wei, 2019. "A generalized free-matrix-based integral inequality for stability analysis of time-varying delay systems," Applied Mathematics and Computation, Elsevier, vol. 354(C), pages 1-8.
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    Cited by:

    1. Man-Wen Tian & Shu-Rong Yan & Jinping Liu & Khalid A. Alattas & Ardashir Mohammadzadeh & Mai The Vu, 2022. "A New Type-3 Fuzzy Logic Approach for Chaotic Systems: Robust Learning Algorithm," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    2. Tingting Tian & Xiaorong Hou & Fang Yan, 2022. "A Novel MRAC Scheme for Output Tracking," Mathematics, MDPI, vol. 10(14), pages 1-11, July.

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