One Equation to Rule Them All -- Part II: Direct Data-Driven Reduction and Regulation

TL;DR

This paper extends a data-driven framework based on the Sylvester equation to address control problems like model order reduction and output regulation, providing solutions from measurements and analyzing noise effects.

Contribution

It introduces novel data-driven methods for model reduction and output regulation based on the Sylvester equation, advancing control design without explicit models.

Findings

Data-driven model reduction methods from input-output and input-state measurements

Solutions for static and dynamic output regulation using data

Analysis of noise impact on data-driven control procedures

Abstract

The Sylvester equation underpins a wide spectrum of control synthesis and systems analysis tools associated with cascade interconnections. In the preceding Part I [1] of this article, it was shown that such an equation can be reformulated using data, enabling the production of a collection of data-driven stabilisation procedures. In this second part of the article, we continue to develop the framework established in Part I to solve two important control-theoretic problems: model order reduction and output regulation. For the model order reduction problem we provide a solution from input-state measurements, from input-output measurements, and we study the effect of the noise. For the output regulation problem, we provide data-driven solutions for the static and dynamic feedback problem. The proposed designs are illustrated by means of examples.