Data-driven Structured Realization

TL;DR

This paper introduces a data-driven framework for constructing structured linear dynamical system models from transfer function measurements, extending the Loewner realization method to more complex system structures including delays and higher-order systems.

Contribution

It extends the Loewner realization framework to handle structured systems with prescribed functions, enabling data-driven modeling of complex dynamical systems.

Findings

Successfully constructs structured realizations from transfer function data.

Applicable to second-order, delay, and higher-order systems.

Numerical examples demonstrate effectiveness and advantages.

Abstract

We present a framework for constructing structured realizations of linear dynamical systems having transfer functions of the form $C(\sum_{k=1}^K h_k(s)A_k)^{-1}B$ where $h_1,h_2,\ldots,h_K$ are prescribed functions that specify the surmised structure of the model. Our construction is data-driven in the sense that an interpolant is derived entirely from measurements of a transfer function. Our approach extends the Loewner realization framework to more general system structure that includes second-order (and higher) systems as well as systems with internal delays. Numerical examples demonstrate the advantages of this approach.