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Observer-based sliding mode control for stochastic hyperbolic PDE systems with quantized output signal

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  • Song, Xiaona
  • Wang, Mi
  • Song, Shuai
  • Wang, Zhen

Abstract

In this note, a sliding mode control scheme is firstly developed for a class of stochastic hyperbolic partial differential equation (PDE) systems. Initially, it is assumed that the considered systems’ states are unavailable for the controller, thus a new state observer is designed. Furthermore, to save the communication resources in network, the system’s measure output signal is quantized before transmission, based on which a novel sliding mode controller is constructed to enhance the system’s robustness. Then, some new criteria that guarantee the systems’ stability and H∞ disturbance attenuation performance are established in terms of linear matrix inequality. In the end, two simulation studies are presented to demonstrate the effectiveness of the developed control strategy.

Suggested Citation

  • Song, Xiaona & Wang, Mi & Song, Shuai & Wang, Zhen, 2021. "Observer-based sliding mode control for stochastic hyperbolic PDE systems with quantized output signal," Applied Mathematics and Computation, Elsevier, vol. 393(C).
    • Handle: RePEc:eee:apmaco:v:393:y:2021:i:c:s009630032030597x
    DOI: 10.1016/j.amc.2020.125643
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    References listed on IDEAS

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    1. Song, Xiaona & Wang, Mi & Song, Shuai & Wang, Zhen, 2019. "Quantized output feedback control for nonlinear Markovian jump distributed parameter systems with unreliable communication links," Applied Mathematics and Computation, Elsevier, vol. 353(C), pages 371-395.
    2. Faragó, István & Karátson, János & Korotov, Sergey, 2017. "Discrete nonnegativity for nonlinear cooperative parabolic PDE systems with non-monotone coupling," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 139(C), pages 37-53.
    3. Wang, Xuelian & Xia, Jianwei & Wang, Jing & Wang, Jian & Wang, Zhen, 2019. "Passive state estimation for fuzzy jumping neural networks with fading channels based on the hidden Markov model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    4. Пигнастый, Олег & Koжевников, Георгий, 2019. "Распределенная Динамическая Pde-Модель Программного Управления Загрузкой Технологического Оборудования Производственной Линии [Distributed dynamic PDE-model of a program control by utilization of t," MPRA Paper 93278, University Library of Munich, Germany, revised 02 Feb 2019.
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    Cited by:

    1. Mahmoodabadi, M.J., 2023. "An optimal robust fuzzy adaptive integral sliding mode controller based upon a multi-objective grey wolf optimization algorithm for a nonlinear uncertain chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 167(C).
    2. Song, Xiaona & Zhang, Renzhi & Song, Shuai & Zhang, Yijun, 2022. "Fuzzy adaptive-event-triggered control for semi-linear parabolic PDE systems with stochastic actuator failures," Applied Mathematics and Computation, Elsevier, vol. 426(C).

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