Robust Online Convex Optimization for Disturbance Rejection
Abstract
Online convex optimization (OCO) is a powerful tool for learning sequential data, making it ideal for high precision control applications where the disturbances are arbitrary and unknown in advance. However, the ability of OCO-based controllers to accurately learn the disturbance while maintaining closed-loop stability relies on having an accurate model of the plant. This paper studies the performance of OCO-based controllers for linear time-invariant (LTI) systems subject to disturbance and model uncertainty. The model uncertainty can cause the closed-loop to become unstable. We provide a sufficient condition for robust stability based on the small gain theorem. This condition is easily incorporated as an on-line constraint in the OCO controller. Finally, we verify via numerical simulations that imposing the robust stability condition on the OCO controller ensures closed-loop stability.
Cite
@article{arxiv.2405.07037,
title = {Robust Online Convex Optimization for Disturbance Rejection},
author = {Joyce Lai and Peter Seiler},
journal= {arXiv preprint arXiv:2405.07037},
year = {2024}
}