Symmetric Hermite quadrature-based balanced truncation for learning linear dynamical systems from derivative data

2026-05-29

AI Summary

This work addresses the problem of constructing linear reduced-order models from sampled data of a system’s transfer function and its derivatives while preserving essential structural properties. The authors propose a novel approach that integrates symmetric Hermite quadrature with balanced truncation. By leveraging sampled information of the transfer function and its derivatives, and incorporating a symmetric Hermite quadrature formula, the method rigorously preserves key characteristics of the original system—such as state-space Hermiticity and asymptotic stability—throughout the reduction process. The resulting reduced-order models not only achieve high-fidelity approximation of the full-order system’s dynamic response but also guarantee stability and physical consistency, thereby significantly enhancing the structure-preserving capability of data-driven model reduction.

Abstract

Data-driven reduced-order modeling is an essential component in the computer-aided design of control systems. In this work, we present a novel symmetric Hermite formulation of the quadrature-based balanced truncation algorithm that constructs linear reduced-order models from evaluations of the full-order system's transfer function and its derivative. Significantly, the Hermite formulation preserves desirable qualitative properties of the system used to generate the data, such as state-space Hermiticity and, consequently, asymptotic stability.

Problem

• reduced-order modeling
• linear dynamical systems
• derivative data
• asymptotic stability
• Hermiticity

Innovation

• symmetric Hermite quadrature
• balanced truncation
• derivative data
• reduced-order modeling
• asymptotic stability