Combining Prior Knowledge and Data for Robust Controller Design

TL;DR

This paper introduces a systematic framework that combines prior knowledge and data for designing robust controllers for linear and nonlinear systems, ensuring stability and performance with reduced conservatism.

Contribution

It develops LMI-based feasibility criteria that integrate prior knowledge and data, including a novel disturbance description, extending to output-feedback and nonlinear uncertainties.

Findings

Reduces conservatism compared to black-box data-driven control.

Guarantees stability and performance for systems consistent with prior knowledge and data.

Demonstrates improved control performance through numerical examples.

Abstract

We present a framework for systematically combining data of an unknown linear time-invariant system with prior knowledge on the system matrices or on the uncertainty for robust controller design. Our approach leads to linear matrix inequality (LMI) based feasibility criteria which guarantee stability and performance robustly for all closed-loop systems consistent with the prior knowledge and the available data. The design procedures rely on a combination of multipliers inferred via prior knowledge and learnt from measured data, where for the latter a novel and unifying disturbance description is employed. While large parts of the paper focus on linear systems and input-state measurements, we also provide extensions to robust output-feedback design based on noisy input-output data and against nonlinear uncertainties. We illustrate through numerical examples that our approach provides a flexible framework for simultaneously leveraging prior knowledge and data, thereby reducing conservatism and improving performance significantly if compared to black-box approaches to data-driven control.