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.
| Comments: | 31 pages, 5 figures, 5 tables |
| Subjects: | Numerical Analysis (math.NA); Systems and Control (eess.SY); Dynamical Systems (math.DS); Optimization and Control (math.OC) |
| MSC classes: | 37N35, 65F55, 93A15, 93B15, 93C57 |
| Cite as: | arXiv:2506.10118 [math.NA] |
| (or arXiv:2506.10118v2 [math.NA] for this version) | |
| https://doi.org/10.48550/arXiv.2506.10118 arXiv-issued DOI via DataCite |
From: Sean Reiter [view email]
[v1]
Wed, 11 Jun 2025 18:58:22 UTC (763 KB)
[v2]
Fri, 22 May 2026 16:37:13 UTC (1,218 KB)
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