Abstract: This paper addresses the problem of iterative learning control for systems in the presence of a fixed initial shift. A feedback-aided PD-type learning algorithm is proposed, and the convergence analysis indicates that such a learning algorithm can ensure that the tracking error achieves asymptotic convergence with respect to time, as the iteration approaches infinity. Furthermore, the initial rectifying and terminal converging strategies are adopted respectively to form learning algorithms for eliminating the effect of the fixed initial shift. It is shown that the system output converges to the desired trajectory over a pre-specified time interval no matter what value the fixed initial shift takes. Numerical results are presented to demonstrate the effectiveness of the proposed learning algorithms.