Robust Online Convex Optimization for Disturbance Rejection

TL;DR

This paper develops a robust online convex optimization framework for linear systems that ensures disturbance rejection and stability despite model uncertainties, verified through numerical simulations.

Contribution

It introduces a sufficient stability condition integrated into OCO controllers to handle model uncertainty and disturbance in linear systems.

Findings

The proposed method guarantees closed-loop stability under certain conditions.

Numerical simulations confirm the effectiveness of the robust stability constraint.

The approach enhances disturbance rejection capabilities in uncertain linear systems.

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.