Learning-enhanced robust controller synthesis with rigorous statistical and control-theoretic guarantees

TL;DR

This paper introduces a framework combining machine learning with robust control, ensuring rigorous guarantees while improving performance through data-driven methods.

Contribution

It presents a systematic approach integrating Gaussian Process Regression into robust control synthesis with formal guarantees.

Findings

Improved control performance with more data

Guarantees maintained throughout learning process

Framework compatible with existing robust control methods

Abstract

The combination of machine learning with control offers many opportunities, in particular for robust control. However, due to strong safety and reliability requirements in many real-world applications, providing rigorous statistical and control-theoretic guarantees is of utmost importance, yet difficult to achieve for learning-based control schemes. We present a general framework for learning-enhanced robust control that allows for systematic integration of prior engineering knowledge, is fully compatible with modern robust control and still comes with rigorous and practically meaningful guarantees. Building on the established Linear Fractional Representation and Integral Quadratic Constraints framework, we integrate Gaussian Process Regression as a learning component and state-of-the-art robust controller synthesis. In a concrete robust control example, our approach is demonstrated to yield improved performance with more data, while guarantees are maintained throughout.