Self-correcting iterative learning-based fault estimation for parabolic distributed parameter systems

This brief presents a novel method for simultaneously estimating time-domain faults and spatio-temporal faults in parabolic distributed parameter systems (PDPSs). Initially, an iterative learning observer that considers both temporal and spatial variations is developed to estimate faults in PDPS. Subsequently, a novel self-correcting iterative learning (SCIL)-based fault estimation law is designed to enhance the speed and accuracy of fault estimation. Meanwhile, by employing the λ-norm method, L2-norm method, and mathematical induction method, it becomes feasible to derive the convergence conditions and obtain the gain matrices in a straightforward manner. Finally, simulation results are provided to verify the applicability of the developed method, demonstrating its capability to estimate complex fault modes and its superior performance in fault estimation.