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This paper presents an extension method of iterative learning control (ILC) to address the applications associated with non-repetitive time-varying systems (NTVSs). Conventional ILC approaches employ fixed nominal system models, but non-repetitive time-varying models may lead to accumulated model uncertainties, which fails to satisfy the robust convergence conditions. To tackle this issue, a novel ILC algorithm with parameter estimation is proposed using back propagation neural network. This algorithm incorporates an approach that utilizes Bayesian regularization training mechanism to accurately estimate non-repetitive time-varying parameters. Through comprehensive experiment on Monolithic XY Stage, the performance of proposed algorithm is validated to demonstrate its feasibility and effectiveness while handling tasks on NTVSs. [ABSTRACT FROM AUTHOR]