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arXiv · 2506.10118

Data-driven balanced truncation for second-order systems with generalized proportional damping

Sean Reiter·Steffen W. R. Werner
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Abstract

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop a new approach for the structured data-driven surrogate modeling of linear dynamical systems described by second-order time derivatives via balanced truncation model-order reduction. The proposed method is a data-driven reformulation of position-velocity balanced truncation for second-order systems and generalizes the quadrature-based balanced truncation for unstructured first-order systems to the second-order case. The computed surrogates encode a generalized proportional damping structure, and we propose a computational procedure for inferring the damping coefficients from data by minimizing a least-squares error over the coefficients. Several numerical examples demonstrate the effectiveness of the proposed method.

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Sean Reiter, Steffen W. R. Werner. 2026-05-22. Data-driven balanced truncation for second-order systems with generalized proportional damping. https://doi.org/10.1137/25m1768217

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