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In this work, an adaptive iterative learning control (AILC) method is designed for a class of parametric discrete‐time nonlinear systems with random initial condition, unknown time‐varying input gain and multiple time‐iteration‐varying factors including multiple unknown time‐iteration‐varying parameters and unknown time‐iteration‐varying external disturbance. The iteration‐varying factors can be generated by virtue of multiple iteration‐varying high‐order internal models, respectively, where iteration‐varying high‐order internal model means it has iteration‐varying order or coefficients. Moreover, the parameter updating law is designed based on the recursive least squares algorithm. Using the designed AILC based on iteration‐varying high‐order internal model, the learning convergence in the iteration domain is guaranteed through rigorous theoretical analysis under Lyapunov theory. Finally, two simulation examples are given to demonstrate that the proposed scheme is effective. [ABSTRACT FROM AUTHOR]