An Improved Iterative Learning Method for Fault Estimation in Nonlinear Parabolic Distributed Parameter System

This paper explores the fault estimation (FE) problem in spatial-temporal parabolic distributed parameter systems (PDPS). Firstly, a nonlinear iterative learning observer (NILO) is designed to incorporate both temporal and spatial variations for accurate fault estimation. Subsequently, an improved iterative learning algorithm is introduced to enhance fault estimation speed and accuracy. By means of rigorous theoretical analysis, it is demonstrated that the fault estimation error converges under the (L<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>, λ)-norm. Finally, numerical simulations of two fault signals are presented to validate the performance of the proposed fault estimation algorithm.