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A Fuzzy Design for a Sliding Mode Observer-Based Control Scheme of Takagi-Sugeno Markov Jump Systems under Imperfect Premise Matching with Bio-Economic and Industrial Applications

Author

Listed:
  • Obaid Alshammari

    (Department of Electrical Engineering, College of Engineering, University of Ha’il, Hail 2440, Saudi Arabia)

  • Mourad Kchaou

    (Department of Electrical Engineering, College of Engineering, University of Ha’il, Hail 2440, Saudi Arabia
    Lab-STA, LR11ES50, National School of Engineering of Sfax, University of Sfax, Sfax 3029, Tunisia)

  • Houssem Jerbi

    (Department of Industrial Engineering, College of Engineering, University of Ha’il, Hail 2440, Saudi Arabia)

  • Sondess Ben Aoun

    (Department of Computer Engineering, College of Computer Science and Engineering, University of Ha’il, Hail 2440, Saudi Arabia)

  • Víctor Leiva

    (School of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, Chile)

Abstract

Fuzzy theory is widely studied and applied. This article introduces an adaptive control scheme for a class of non-linear systems with Markov jump switching. The introduced scheme supposes that the system is submitted to external disturbances under imperfect premise matching. By using discrete-time Takagi–Sugeno fuzzy models, a sliding mode observer-based control scheme is utilized to estimate unmeasured states of the system. We build two fuzzy switching manifolds for the disturbance and sliding mode observer systems. Then, a linear matrix inequality-based criterion is developed using slack matrices. This criterion proves that the sliding mode dynamics are robustly admissible under an H-infinity performance often used in control theory. Hence, new adaptive sliding mode controllers are synthesized for the disturbance and sliding mode observer systems. This allows the reachability of pre-designed sliding surfaces to be guaranteed. Finally, experimental numerical illustrations on a bio-economic system and a tunnel diode circuit are presented to show potential applications, as well as validating the effectiveness of the scheme proposed in the present investigation.

Suggested Citation

  • Obaid Alshammari & Mourad Kchaou & Houssem Jerbi & Sondess Ben Aoun & Víctor Leiva, 2022. "A Fuzzy Design for a Sliding Mode Observer-Based Control Scheme of Takagi-Sugeno Markov Jump Systems under Imperfect Premise Matching with Bio-Economic and Industrial Applications," Mathematics, MDPI, vol. 10(18), pages 1-28, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:18:p:3309-:d:912917
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    References listed on IDEAS

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    1. Hanen Chaouch & Samia Charfeddine & Sondess Ben Aoun & Houssem Jerbi & Víctor Leiva, 2022. "Multiscale Monitoring Using Machine Learning Methods: New Methodology and an Industrial Application to a Photovoltaic System," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    2. Tat-Bao-Thien Nguyen & Teh-Lu Liao & Jun-Juh Yan, 2015. "Improved Adaptive Sliding Mode Control for a Class of Uncertain Nonlinear Systems Subjected to Input Nonlinearity via Fuzzy Neural Networks," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, April.
    3. Yueqiao Han & Yonggui Kao & Cunchen Gao & Baoping Jiang, 2017. "Robust sliding mode control for uncertain discrete singular systems with time-varying delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(4), pages 818-827, March.
    4. Samia Charfeddine & Hadeel Alharbi & Houssem Jerbi & Mourad Kchaou & Rabeh Abbassi & Víctor Leiva, 2022. "A Stochastic Optimization Algorithm to Enhance Controllers of Photovoltaic Systems," Mathematics, MDPI, vol. 10(12), pages 1-26, June.
    5. Zhan Su & Jun Ai & Qingling Zhang & Naixue Xiong, 2017. "An improved robust finite-time dissipative control for uncertain fuzzy descriptor systems with disturbance," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(8), pages 1581-1596, June.
    6. Jiang, Baoping & Gao, Cunchen & Xie, Jing, 2015. "Passivity based sliding mode control of uncertain singular Markovian jump systems with time-varying delay and nonlinear perturbations," Applied Mathematics and Computation, Elsevier, vol. 271(C), pages 187-200.
    7. Chen, Jian & Lin, Chong & Chen, Bing & Wang, Qing-Guo, 2017. "Mixed H∞ and passive control for singular systems with time delay via static output feedback," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 244-253.
    8. Mourad Kchaou & Ahmed El-Hajjaji, 2017. "Resilient sliding mode control for discrete-time descriptor fuzzy systems with multiple time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(2), pages 288-301, January.
    9. Li, Rongchang & Zhang, Qingling, 2018. "Robust H∞ sliding mode observer design for a class of Takagi–Sugeno fuzzy descriptor systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 337(C), pages 158-178.
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