Data-driven modeling and control of large-scale dynamical systems in the Loewner framework

TL;DR

This paper reviews the Loewner framework, a data-driven method for modeling and reducing large-scale dynamical systems, highlighting recent extensions to complex systems and practical control applications.

Contribution

It provides an overview of recent extensions of the Loewner framework to nonlinear and parametric systems, along with practical test case applications.

Findings

Effective data-driven model reduction for large-scale systems

Application to control design and feedback controller synthesis

Demonstrated success on practical test cases

Abstract

In this contribution, we discuss the modeling and model reduction framework known as the Loewner framework. This is a data-driven approach, applicable to large-scale systems, which was originally developed for applications to linear time-invariant systems. In recent years, this method has been extended to a number of additional more complex scenarios, including linear parametric or nonlinear dynamical systems. We will provide here an overview of the latter two, together with time-domain extensions. Additionally, the application of the Loewner framework is illustrated by a collection of practical test cases. Firstly, for data-driven complexity reduction of the underlying model, and secondly, for dealing with control applications of complex systems (in particular, with feedback controller design).