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Spatiotemporal fault detection, estimation and control for nonlinear reaction-diffusion equations

Author

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  • Lei, Yanfang
  • Li, Junmin
  • Zhao, Ailiang

Abstract

This work is devoted to the study of spatiotemporal fault detection, estimation and control for nonlinear reaction-diffusion equations (RDEs). This strategy mainly includes the following three steps. Firstly, a fault detection observer is constructed by using average measurement, and the deviation signal generated by the observer is used to detect the existence of the fault. Secondly, a partial differential equation (PDE) fault estimator with a fault estimation algorithm is designed, which starts to perform only when the fault observer detects the existence of a fault. Thirdly, a feedback controller based on PDE fault estimator is designed to make the coupled system globally ultimately uniformly bounded (UUB). Sufficient conditions in terms of linear matrix inequalities (LMIs) are derived to ensure the coupled system globally UUB by using the Lyapunov-Krasovskii method. Finally, simulation examples are carried out to illustrate the validity of the proposed fault estimation algorithm and the designed controller.

Suggested Citation

  • Lei, Yanfang & Li, Junmin & Zhao, Ailiang, 2022. "Spatiotemporal fault detection, estimation and control for nonlinear reaction-diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    • Handle: RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009425
    DOI: 10.1016/j.amc.2021.126859
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    References listed on IDEAS

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    1. Du, Dongsheng, 2017. "Fault detection for discrete-time linear systems based on descriptor observer approach," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 575-585.
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