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Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach

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  • Mobayen, Saleh
  • Alattas, Khalid A.
  • Fekih, Afef
  • El-Sousy, Fayez F.M.
  • Bakouri, Mohsen

Abstract

In this study, a novel barrier function-based adaptive non-singular terminal sliding mode control methodology is suggested for robust stability of disturbed nonlinear systems. It is proved that the barrier function-based control method can force the state trajectories to converge to a region near origin in the finite time. A sufficient criterion is derived using Lyapunov stability theorem and linear matrix inequalities (LMIs) to satisfy the asymptotic stability of state trajectories. In addition, the design eliminates the necessity to have any knowledge about the upper bounds of external disturbances; a common requirement in sliding mode control implementation. The stability analysis verifies that the system states, under the designed control scheme, can asymptotically converge to a pre-defined region. Lastly, simulation studies are presented to confirm the efficacy and robustness of proposed approach.

Suggested Citation

  • Mobayen, Saleh & Alattas, Khalid A. & Fekih, Afef & El-Sousy, Fayez F.M. & Bakouri, Mohsen, 2022. "Barrier function-based adaptive nonsingular sliding mode control of disturbed nonlinear systems: A linear matrix inequality approach," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    • Handle: RePEc:eee:chsofr:v:157:y:2022:i:c:s096007792200128x
    DOI: 10.1016/j.chaos.2022.111918
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    References listed on IDEAS

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    1. Wang, Yang & Wang, Zhen & Chen, Mingshu & Kong, Lingyun, 2021. "Predefined-time sliding mode formation control for multiple autonomous underwater vehicles with uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Yao, Qijia, 2021. "Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    3. Jafari, Sajad & Sprott, J.C., 2013. "Simple chaotic flows with a line equilibrium," Chaos, Solitons & Fractals, Elsevier, vol. 57(C), pages 79-84.
    4. Sharafian, Amin & Sharifi, Alireza & Zhang, Weidong, 2020. "Different types of sliding mode controller for nonlinear fractional multi-Agent system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Yousefpour, Amin & Jahanshahi, Hadi & Munoz-Pacheco, Jesus M. & Bekiros, Stelios & Wei, Zhouchao, 2020. "A fractional-order hyper-chaotic economic system with transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
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    Citations

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    Cited by:

    1. Sun, Meng & Zhuang, Guangming & Xia, Jianwei & Wang, Yanqian & Chen, Guoliang, 2022. "Stochastic admissibility and H∞ output feedback control for singular Markov jump systems under dynamic measurement output event-triggered strategy," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Yassine Bouteraa & Javad Mostafaee & Mourad Kchaou & Rabeh Abbassi & Houssem Jerbi & Saleh Mobayen, 2022. "A New Simple Chaotic System with One Nonlinear Term," Mathematics, MDPI, vol. 10(22), pages 1-17, November.
    3. Zhang, Xin & Shi, Ran, 2022. "Novel fast fixed-time sliding mode trajectory tracking control for manipulator," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    4. Masoud Chatavi & Mai The Vu & Saleh Mobayen & Afef Fekih, 2022. "H ∞ Robust LMI-Based Nonlinear State Feedback Controller of Uncertain Nonlinear Systems with External Disturbances," Mathematics, MDPI, vol. 10(19), pages 1-19, September.
    5. Mousavi, Yashar & Bevan, Geraint & Kucukdemiral, Ibrahim Beklan & Fekih, Afef, 2022. "Sliding mode control of wind energy conversion systems: Trends and applications," Renewable and Sustainable Energy Reviews, Elsevier, vol. 167(C).

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