Iterative learning control for repetitive tasks with randomly varying trial lengths using successive projection

This article proposes an effective iterative learning control (ILC) approach based on successive projection scheme for repetitive systems with randomly varying trial lengths. A modified ILC problem is formulated to extend the classical ILC task description to incorporate a randomly varying trial length, while its design objective considers the mathematical expectation of its tracking error to evaluate the task performance. To solve this problem, this article employs the successive projection framework to give an iterative input signal update law by defining the corresponding convex sets based on the design requirements. This update law further yields an ILC algorithm, whose convergence properties are proved to be held under mild conditions. In addition, the input signal constraint can be embedded into the design without violating the convergence properties to obtain an alternative algorithm. The performance of the proposed algorithms is verified using a numerical model to show the effectiveness at occasions with and without input constraints.