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

•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.•A 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.•Sufficient conditions in terms of LMIs are derived to ensure the coupled system globally UUB by using the Lyapunov-Krasovskii method, and then a feedback controller based on PDE fault estimator is designed. Furthermore, simulation examples are carried out to illustrate the validity of the proposed fault estimation algorithm and the designed controller.