Spatiotemporal fault estimation for switched nonlinear reaction–diffusion systems via adaptive iterative learning

In this paper, an iterative learning-based spatiotemporal fault estimation issue in switched reaction–diffusion systems is investigated. Initially, average dwell-time switching rules are utilized to describe a class of switched reaction–diffusion systems characterized by mode jumps. Then, different from the existing fault estimation methods, a fault estimator is designed for spatiotemporal faults to realize an accurate estimation of faults by using the iterative learning strategy. Subsequently, to improve the speed of fault estimation, an adaptive iterative learning-based fault estimation law is proposed, which can achieve faster fault estimation by continuously adjusting the iterative learning gain. Moreover, sufficient conditions for the convergence of the fault estimation error are obtained by using the $\lambda$-norm and the mathematical induction methods. Finally, an illustrative example is presented to check the practicality and superiority of the proposed fault estimation scheme.