Safety Filter for Robust Disturbance Rejection via Online Optimization

TL;DR

This paper presents a safety filter using adaptive FIR filtering to enhance the robustness of disturbance rejection in high-precision control, ensuring stability despite model uncertainties by minimally modifying online optimization commands.

Contribution

It introduces a novel safety filter that enforces robust stability constraints on FIR coefficients, enabling stable disturbance rejection in systems employing online convex optimization.

Findings

The safety filter guarantees robust stability under model uncertainties.

It allows for easy online implementation by directly limiting OCO commands.

The method provides a tunable trade-off between robustness and performance.

Abstract

Disturbance rejection in high-precision control applications can be significantly improved upon via online convex optimization (OCO). This includes classical techniques such as recursive least squares (RLS) and more recent, regret-based formulations. However, these methods can cause instabilities in the presence of model uncertainty. This paper introduces a safety filter for systems with OCO in the form of adaptive finite impulse response (FIR) filtering to ensure robust disturbance rejection. The safety filter enforces a robust stability constraint on the FIR coefficients while minimally altering the OCO command in the $\infty$-norm cost. Additionally, we show that the induced $\ell_\infty$-norm allows for easy online implementation of the safety filter by directly limiting the OCO command. The constraint can be tuned to trade off robustness and performance. We provide a simple example to demonstrate the safety filter.