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Resilient observer-based unified state and fault estimation for nonlinear parabolic PDE systems via fuzzy approach over finite-time interval

Author

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  • Elayabharath, V.T.
  • Sozhaeswari, P.
  • Tatar, N.
  • Sakthivel, R.
  • Satheesh, T.

Abstract

With the aid of a resilient fuzzy observer, this study delves into the investigation of finite-time state and fault estimation for parabolic-type nonlinear PDE systems described by fuzzy models with faults and external disturbances. Primarily, a fuzzy-dependent observer is built to offer precise estimations of the states and faults simultaneously. Therein, the fluctuations that exhibit random character are taken into account in the observer gain, which enhances the resiliency of the configured fuzzy observer. Meanwhile, the phenomenon of randomly occurring gain fluctuations is effectively characterized by utilizing a random variable that adheres to the Bernoulli distribution. Subsequently, by employing the Lyapunov stability theory and the integral-based Wirtinger's inequality, a set of adequate criteria is obtained in the form of linear matrix inequalities to ascertain that both the state and fault estimation errors are stable in a finite-time with a gratified extended passivity performance index. In the meantime, the observer gain matrices can be obtained by relying on the developed criteria. Ultimately, the simulation results of the Fisher equation are offered to emphasize the superiority of the developed resilient fuzzy observer-based approach.

Suggested Citation

  • Elayabharath, V.T. & Sozhaeswari, P. & Tatar, N. & Sakthivel, R. & Satheesh, T., 2025. "Resilient observer-based unified state and fault estimation for nonlinear parabolic PDE systems via fuzzy approach over finite-time interval," Applied Mathematics and Computation, Elsevier, vol. 488(C).
    • Handle: RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005861
    DOI: 10.1016/j.amc.2024.129125
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    References listed on IDEAS

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    1. Han, Xin-Xin & Wu, Kai-Ning & Ding, Xiaohua, 2020. "Finite-time stabilization for stochastic reaction-diffusion systems with Markovian switching via boundary control," Applied Mathematics and Computation, Elsevier, vol. 385(C).
    2. Zhu, Baopeng & Wang, Yingchun & Zhang, Huaguang & Xie, Xiangpeng, 2021. "Distributed finite-time fault estimation and fault-tolerant control for cyber-physical systems with matched uncertainties," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Xuefeng Zhang & Jin-Xi Zhang & Wenkai Huang & Peng Shi, 2023. "Non-fragile sliding mode observer based fault estimation for interval type-2 fuzzy singular fractional order systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 54(7), pages 1451-1470, May.
    4. 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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