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

Highlights：

• 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.