From Data $H(j\omega_i)$ to Balanced Truncation Family: A Projection-based Non-intrusive Approach

TL;DR

This paper introduces a non-intrusive, data-driven approach for balanced truncation and its variants, relying solely on transfer function samples on the imaginary axis, avoiding spectral factorizations.

Contribution

It develops a projection-based framework enabling non-intrusive implementations of various balanced truncation methods using measurable transfer function data.

Findings

Achieves performance comparable to traditional intrusive methods.

Accurately captures dominant Hankel singular values.

Applicable to multiple balanced truncation variants.

Abstract

This paper presents data-driven implementations of balanced truncation and several of its generalizations that rely exclusively on transfer function samples on the imaginary axis. Rather than implicitly approximating the Gramians via numerical quadrature, the proposed approach approximates them implicitly through projection. This enables multiple members of the balanced truncation family to be implemented non-intrusively using practically measurable data, without requiring spectral factorizations. Using this projection-based framework, data-driven implementations are developed for standard balanced truncation, frequency-limited balanced truncation, time-limited balanced truncation, self-weighted balanced truncation, LQG balanced truncation, H-infinity balanced truncation, positive-real balanced truncation, bounded-real balanced truncation, and stochastic balanced truncation. Numerical results demonstrate that the proposed non-intrusive implementations achieve performance comparable to their intrusive counterparts and accurately capture the dominant Hankel singular values.