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

TL;DR

This paper analyzes the performance of online gradient descent in iterative learning control with model mismatch, focusing on regret bounds and limitations, supported by numerical simulations.

Contribution

It introduces a regret-based analysis framework for ILC with model mismatch using online learning concepts, highlighting fundamental limitations and potential integration with adaptation.

Findings

Performance bounds for online gradient descent in ILC

Identification of fundamental limitations of the scheme

Numerical validation on benchmark ILC problem

Abstract

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.