# Regret Analysis of Online Gradient Descent-based Iterative Learning Control with Model Mismatch

arXiv: https://arxiv.org/abs/2204.04722 · HTML: https://mlsanity.com/paper/2204.04722/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 10 Apr 2022.

## Builds on (most cited first, 9 of 9)

- [Introduction to Online Convex Optimization](https://mlsanity.com/paper/1909.05207/) (2019)
- [Online Optimization : Competing with Dynamic Comparators](https://mlsanity.com/paper/1501.06225/) (2015)
- [The Nonstochastic Control Problem](https://mlsanity.com/paper/1911.12178/) (2019)
- [Dynamical Models and Tracking Regret in Online Convex Programming](https://mlsanity.com/paper/1301.1254/) (2013)
- [Online Learning with Inexact Proximal Online Gradient Descent Algorithms](https://mlsanity.com/paper/1806.00202/) (2018)
- [A Regret Minimization Approach to Iterative Learning Control](https://mlsanity.com/paper/2102.13478/) (2021)
- [Safe Control with Minimal Regret](https://mlsanity.com/paper/2203.00358/) (2022)
- [Regret-optimal control in dynamic environments](https://mlsanity.com/paper/2010.10473/) (2020)
- [On Robustness in Optimization-Based Constrained Iterative Learning Control](https://mlsanity.com/paper/2203.05291/) (2022)

## Built on by (most cited first, 1 of 1)

- [Predictive Linear Online Tracking for Unknown Targets](https://mlsanity.com/paper/2402.10036/) (2024)

## Abstract (arXiv)

In Iterative Learning Control (ILC), a sequence of feedforward control actions is generated at each iteration on the basis of partial model knowledge and past measurements with the goal of steering the system toward a desired reference trajectory. This is framed here as an online learning task, where the decision-maker takes sequential decisions by solving a sequence of optimization problems having only partial knowledge of the cost functions. Having established this connection, the performance of an online gradient-descent based scheme using inexact gradient information is analyzed in the setting of dynamic and static regret, standard measures in online learning. Fundamental limitations of the scheme and its integration with adaptation mechanisms are further investigated, followed by numerical simulations on a benchmark ILC problem.