Source data for: 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.

本文针对试验长度非均匀的离散时间系统，采用交替投影法构建了一种新颖的迭代学习控制（Iterative Learning Control，ILC）设计框架。相较于现有针对试验长度非均匀问题的研究成果，本文采用希尔伯特空间（Hilbert space）设定，因此可将试验长度非均匀的线性离散时间系统动力学表征为多个仿射子空间（affine subspaces，或线性流形linear varieties）。受两个闭凸集之间的逐次投影设计思路启发，本文所研究的ILC问题可转化为多集合间的交替投影问题，进而借助希尔伯特空间设定推导关键的系统理论性质。此外，本文针对试验长度非均匀的系统提出了最优ILC设计方案，并将其推广至输入约束场景。文末通过数值案例验证了所提新设计方案的适用性。