Data-driven balancing of linear dynamical systems

TL;DR

This paper introduces a new data-driven approach to balanced truncation for model reduction of linear dynamical systems, utilizing measured or computed response data without relying on a specific model realization.

Contribution

It reformulates classical balanced truncation using transfer function or impulse response data, paralleling the Loewner framework, applicable to both continuous and discrete-time systems.

Findings

Effective in both continuous and discrete-time systems

Does not require explicit model realization

Parallels with the Loewner framework

Abstract

We present a novel reformulation of balanced truncation, a classical model reduction method. The principal innovation that we introduce comes through the use of system response data that has been either measured or computed, without reference to any prescribed realization of the original model. Data are represented by sampled values of the transfer function {or the impulse response} corresponding to the original model. We discuss parallels that our approach bears with the Loewner framework, another popular data-driven model reduction method. We illustrate our approach numerically in both continuous-time and discrete-time cases.