In this paper, we present two iterative learning control (ILC) frameworks for tracking problems with specified data points that are desired points at certain time instants. To design ILC systems for such problems, unlike traditional ILC approaches, we first develop an algorithm in which not only the control signal but also the reference trajectory is updated at each trial. We investigate the relationship between the reference trajectory and ILC tracking control as it relates to the rate of convergence. Second, a new ILC scheme is proposed to produce output curves that pass close to the desired points. Here, the control signals are generated by solving an optimal ILC problem with respect to the desired sampling points. One of the key advantages of the proposed approaches is a significant reduction of the computational cost. (c) 2013 Elsevier Ltd. All rights reserved.