In practical applications of iterative learning control (ILC), the repetitive process may end up early by accident during the performance improvement along the trial axis, which yields the nonuniform trial length problem. For such practical systems, input signals are usually constrained because of some certain physical limitations. This article proposes an optimal ILC algorithm for linear time-invariant multiple-input–multiple-output (MIMO) systems with nonuniform trial lengths under input constraints. The optimal ILC framework is specifically modified for the nonuniform trial length problem, where the primal–dual interior point method is introduced to deal with the input constraints. Hence, the constraint handling capability are improved compared with the conventional counterparts for nonuniform trial lengths. Also, the monotonic convergence property of the proposed optimal ILC algorithm is obtained in the sense of mathematical expectation. Finally, the effectiveness of the proposed algorithm is verified on the numerical simulation of a mobile robot.

Iterative learning control (ILC) is a high‐performance technique for repeated control tasks with design postulates on a fixed reference profile and identical initial conditions. However, the tracking performance is only critical at few points in point‐to‐point tasks, and their initial conditions are usually trial‐varying within a certain range in practice, which essentially degrades the performance of conventional ILC algorithms. Therefore, this study reformulates the ILC problem setup for point‐to‐point tasks and considers the effort of trial‐varying initial conditions in algorithm design. To reduce the tracking error, it proposes a worst‐case norm‐optimal problem and reformulates it into a convex optimisation problem using the Lagrange dual approach. In this sense, a robust ILC algorithm is derived based on iteratively solving this problem. The study also shows that the proposed robust ILC is equivalent to conventional norm‐optimal ILC with trial‐varying parameters. A numerical simulation case study is conducted to compare the performance of this algorithm with that of other control algorithms while performing a given point‐to‐point tracking task. The results reveal its efficiency for the specific task and robustness against trial‐varying initial conditions.

In most implementations of iterative learning control (ILC) for trajectory tracking, it is usually required that the trial lengths of different iterations are uniform. However, this requirement may not always be ensured in practical applications. In this paper, a feedback-aided PD-type ILC design for time-varying systems with non-uniform trial lengths is proposed. Although the actual trial lengths are non-uniform, the designed update sequences provide uniform full-length signals for the update process. Meanwhile, information from the most recent valid iterations can be better used than the mechanisms that compensate with hypothesized data, such as zero. Their recursive generation also reduces the storage burden compared to search strategies. The feedback error signal can be additionally used as part of the correction term to improve the system performance compared to the traditional open-loop approaches. Under a deterministic model, the main convergence results are obtained by combining the [ ]-norm technique with the inductive analysis approach. At last, a linear numerical simulation and a nonlinear single-joint robot simulation are performed, respectively, to show that the proposed design can achieve the asymptotic tracking of the desired trajectories for time-varying systems with non-uniform trial lengths.