Work

$\mathcal{H}_\infty$ model order reduction for quadratic output systems

Year: 2025

Type: preprint

Abstract: Linear time-invariant quadratic output (LTIQO) systems generalize linear time-invariant systems to nonlinear regimes. Problems of this class occur in multiple applications naturally, such as port-Hamiltonian systems, optimal control, and stochastical problems. We introduce an $\mathcal{H}_\infty$-norm for LTIQO systems with one or multiple outputs and propose an algorithm to optimize a reduced order model (ROM) to be close in the $\mathcal{H}_\infty$-norm to a given full order model. We illustrate the applicability and the performance with an established numerical example and compare the resulting ROMs with results from balanced truncation and $\mathcal{H}_2$-focussed algorithms.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2505.12529

Authors: Hillebrecht, Birgit, Unger, Benjamin

Institutions: University of Stuttgart, Stuttgart Technical University of Applied Sciences, Karlsruhe Institute of Technology

Language: English

Topic: Model Reduction and Neural Networks

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: International Max Planck Research School for Environmental, Cellular and Molecular Microbiology, Deutsche Forschungsgemeinschaft, International Max Planck Research School for Advanced Methods in Process and Systems Engineering, Singapore Institute of Manufacturing Technology

Awards: G1486546336, G325672550, G7249683039, SFB 1173: Wellenphänomene: Analysis und Numerik, EXC 2075: Datenintegrierte Simulationswissenschaft (SimTech)

OpenAlex ID: W4417301021

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