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.