# Sparse Iterative Learning Control with Application to a Wafer Stage: Achieving Performance, Resource Efficiency, and Task Flexibility

## TL;DR

This paper introduces a convex optimization-based iterative learning control framework that enforces sparsity to improve resource efficiency, disturbance attenuation, and flexibility, demonstrated on a wafer stage application.

## Contribution

It develops a novel sparse ILC framework using convex relaxations, enabling structured control design for resource-efficient and robust performance.

## Key findings

- Effective sparsity enforcement in ILC via convex relaxations.
- Successful application to wafer stage control demonstrating improved resource use.
- Enhanced disturbance attenuation and task flexibility in experimental results.

## Abstract

Trial-varying disturbances are a key concern in Iterative Learning Control (ILC) and may lead to inefficient and expensive implementations and severe performance deterioration. The aim of this paper is to develop a general framework for optimization-based ILC that allows for enforcing additional structure, including sparsity. The proposed method enforces sparsity in a generalized setting through convex relaxations using $\ell_1$ norms. The proposed ILC framework is applied to the optimization of sampling sequences for resource efficient implementation, trial-varying disturbance attenuation, and basis function selection. The framework has a large potential in control applications such as mechatronics, as is confirmed through an application on a wafer stage.