Abstract: Iterative Learning Control (ILC) is an effective way to track a predefined desired trajectory. In many applications, only a few critical values on a few critical time points are important and system output between these critical points is not cared. So the desired trajectory can be updated iteration by iteration for the improvement of convergence rate. The updating desired trajectory only needs to pass these critical points and value. A feasible interpolating method is used to update reference trajectory. Choosing of interpolating parameter is independent from the system and control algorithm. The ILC input is updated using a closed-loop method in which the learning gain can be chosen in more wide ranges and the non-repeating disturbance can be offset more effectively when the system is not well identified. An initial state shifts is common in many applications. The effect of these initial shifts should be analyzed and offset for point-to-point tracking problem. A new ILC scheme which updates both reference trajectory and control input is developed with initial shifts taken into consideration. Convergence and robustness of new ILC is theoretically analyzed and the advantages are shown in numerical experiments.