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An Adaptive Barrier Function Terminal Sliding Mode Controller for Partial Seizure Disease Based on the Pinsky–Rinzel Mathematical Model

Author

Listed:
  • Zahra Mokhtare

    (Department of Electrical Engineering, University of Zanjan, Zanjan 45195-313, Iran
    Zahra Mokhtare and Mai The Vu are the first authors; these authors contributed equally to this work.)

  • Mai The Vu

    (School of Intelligent Mechatronics Engineering, Sejong University, Seoul 05006, Korea
    Zahra Mokhtare and Mai The Vu are the first authors; these authors contributed equally to this work.)

  • Saleh Mobayen

    (Department of Electrical Engineering, University of Zanjan, Zanjan 45195-313, Iran
    Future Technology Research Center, National Yunlin University of Science and Technology, Douliou 64002, Taiwan)

  • Thaned Rojsiraphisal

    (Advanced Research Center for Computational Simulation, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand
    Data Science Research Center, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

Abstract

This paper proposes an adaptive barrier function terminal sliding mode control method for partial seizure based on the Pinsky–Rinzel model. A terminal sliding mode control technique is designed to achieve the convergence of trajectories to the desired value in a finite time, while an adaptive barrier function is used to ensure that the outputs, which are independent of the disturbance boundary, converge to the predetermined zero location. The performance of the proposed approach is checked for the nonlinear two-compartmental Pinsky–Rinzel pyramidal neuron model. The obtained method of the finite time stability, in the presence of uncertainty and disturbance, is proven by the Lyapunov theory. The simulation results confirm the effectiveness of the proposed control scheme. Finite time convergence, robustness, chattering-free dynamics and near-zero error are the advantages of the proposed technique.

Suggested Citation

  • Zahra Mokhtare & Mai The Vu & Saleh Mobayen & Thaned Rojsiraphisal, 2022. "An Adaptive Barrier Function Terminal Sliding Mode Controller for Partial Seizure Disease Based on the Pinsky–Rinzel Mathematical Model," Mathematics, MDPI, vol. 10(16), pages 1-13, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2940-:d:888733
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    References listed on IDEAS

    as
    1. Khalid A. Alattas & Mai The Vu & Omid Mofid & Fayez F. M. El-Sousy & Abdullah K. Alanazi & Jan Awrejcewicz & Saleh Mobayen, 2022. "Adaptive Nonsingular Terminal Sliding Mode Control for Performance Improvement of Perturbed Nonlinear Systems," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    2. Thaned Rojsiraphisal & Saleh Mobayen & Jihad H. Asad & Mai The Vu & Arthur Chang & Jirapong Puangmalai, 2021. "Fast Terminal Sliding Control of Underactuated Robotic Systems Based on Disturbance Observer with Experimental Validation," Mathematics, MDPI, vol. 9(16), pages 1-17, August.
    3. Puangmalai, Jirapong & Tongkum, Jakkrapong & Rojsiraphisal, Thaned, 2020. "Finite-time stability criteria of linear system with non-differentiable time-varying delay via new integral inequality," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 170-186.
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    Cited by:

    1. Fawaz E. Alsaadi & Amirreza Yasami & Christos Volos & Stelios Bekiros & Hadi Jahanshahi, 2023. "A New Fuzzy Reinforcement Learning Method for Effective Chemotherapy," Mathematics, MDPI, vol. 11(2), pages 1-25, January.

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