Towards robustness guarantees for feedback-based optimization

TL;DR

This paper develops a systematic framework using advanced mathematical tools to analyze and guarantee the robust stability of feedback-based online optimization algorithms under disturbances and model uncertainties.

Contribution

It introduces a novel framework combining monotone operator theory, variational inequalities, and robust control to assess and ensure robustness of online optimization algorithms.

Findings

Provides tractable numerical tests for robustness guarantees.

Demonstrates the framework on a power distribution system case study.

Shows robustness of algorithms in the presence of disturbances and uncertainties.

Abstract

Feedback-based online optimization algorithms have gained traction in recent years because of their simple implementation, their ability to reject disturbances in real time, and their increased robustness to model mismatch. While the robustness properties have been observed both in simulation and experimental results, the theoretical analysis in the literature is mostly limited to nominal conditions. In this work, we propose a framework to systematically assess the robust stability of feedback-based online optimization algorithms. We leverage tools from monotone operator theory, variational inequalities and classical robust control to obtain tractable numerical tests that guarantee robust convergence properties of online algorithms in feedback with a physical system, even in the presence of disturbances and model uncertainty. The results are illustrated via an academic example and a case study of a power distribution system.