Robust point-to-point iterative learning control with trial-varying initial conditions

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.