Alternating projection-based iterative learning control for discrete-time systems with non-uniform trial lengths

This article develops a novel framework for iterative learning control (ILC) design of discrete-time systems with non-uniform trial lengths by using the method of alternating projections. In contrast to existing results for the non-uniform trial length problem, this article uses the Hilbert space setting and hence the linear discrete-time system dynamics with non-uniform trial lengths can be represented by multiple affine subspaces (or linear varieties). Motivated by the successive projection design between two closed convex sets, the considered ILC problem can be transformed into alternating projections between multiple sets, then the Hilbert space setting is used to establish key systems theoretic properties. Moreover, an optimal ILC design is developed for systems with non-uniform trial lengths, which is also extended to the case of input constraints. A numerical case study is given to illustrate the applicability of the new design.