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

Yanfang Lei, Junmin Li and Ailiang Zhao

Applied Mathematics and Computation, 2022, vol. 418, issue C

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.

Keywords: Nonlinear reaction-diffusion equations; Fault detection; Fault estimation; Ultimately uniformly bounded (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:418:y:2022:i:c:s0096300321009425

DOI: 10.1016/j.amc.2021.126859

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