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We present a technique for the approximation of a class of Hilbert space-valued maps which arise within the framework of Model Order Reduction for parametric partial differential equations, whose solution map has a meromorphic structure.…

Numerical Analysis · Mathematics 2021-02-19 Davide Pradovera

The iterative rational Krylov algorithm (IRKA) is a commonly used fixed-point iteration developed to minimize the $\mathcal{H}_2$ model order reduction error. In this work, IRKA is recast as a Riemannian gradient descent method with a fixed…

Numerical Analysis · Mathematics 2024-07-11 Petar Mlinarić , Christopher A. Beattie , Zlatko Drmač , Serkan Gugercin

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…

Optimization and Control · Mathematics 2023-09-25 Rebekka S. Beddig , Peter Benner , Ines Dorschky , Timo Reis , Paul Schwerdtner , Matthias Voigt , Steffen W. R. Werner

We present a novel model-order reduction (MOR) method for linear time-invariant systems that preserves passivity and is thus suited for structure-preserving MOR for port-Hamiltonian (pH) systems. Our algorithm exploits the well-known…

Dynamical Systems · Mathematics 2021-08-30 Tobias Breiten , Benjamin Unger

We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our method is based on a novel parameterization that allows us to…

Systems and Control · Electrical Eng. & Systems 2022-06-09 Tim Moser , Paul Schwerdtner , Volker Mehrmann , Matthias Voigt

The iterative rational Krylov algorithm (\textsf{IRKA}) is a popular approach for producing locally optimal reduced-order $\mathcal{H}_2$-approximations to linear time-invariant (LTI) dynamical systems. Overall, \textsf{IRKA} has seen…

Numerical Analysis · Mathematics 2019-11-15 C. Beattie , Z. Drmac , S. Gugercin

We develop a structure-preserving system-theoretic model reduction framework for nonlinear power grid networks. First, via a lifting transformation, we convert the original nonlinear system with trigonometric nonlinearities to an equivalent…

Systems and Control · Electrical Eng. & Systems 2022-03-18 Bita Safaee , Serkan Gugercin

An important class of dynamical systems with several practical applications is linear systems with quadratic outputs. These models have the same state equation as standard linear time-invariant systems but differ in their output equations,…

Systems and Control · Electrical Eng. & Systems 2024-08-13 Umair Zulfiqar , Zhi-Hua Xiao , Qiu-Yan Song , Mohammad Monir Uddin , Victor Sreeram

This paper develops an interpolatory framework for weighted-$\mathcal{H}_2$ model reduction of MIMO dynamical systems. A new representation of the weighted-$\mathcal{H}_2$ inner products in MIMO settings is introduced and used to derive…

Systems and Control · Computer Science 2016-10-05 Tobias Breiten , Christopher Beattie , Serkan Gugercin

A standard approach to reduced-order modeling of higher-order linear dynamical systems is to rewrite the system as an equivalent first-order system and then employ Krylov-subspace techniques for reduced-order modeling of first-order…

Numerical Analysis · Mathematics 2007-05-23 Roland W. Freund

We examine interpolatory model reduction methods that are well-suited for treating large scale port-Hamiltonian differential-algebraic systems in a way that is able to preserve and indeed, take advantage of the underlying structural…

Numerical Analysis · Mathematics 2021-11-03 Chris A. Beattie , Serkan Gugercin , Volker Mehrmann

A model order reduction algorithm is presented that generates a reduced-order model of the original high-order model, which ensures high-fidelity within the desired time interval. The reduced model satisfies a subset of the first-order…

Systems and Control · Electrical Eng. & Systems 2020-07-16 Umair Zulfiqar , Victor Sreeram , Xin Du

We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems in pH form permit energy-based modeling and intuitive…

Optimization and Control · Mathematics 2022-06-06 Paul Schwerdtner , Tim Moser , Volker Mehrmann , Matthias Voigt

This paper presents a structure-preserving model reduction framework for linear systems, in which the $\mathcal{H}_2$ optimization is incorporated with the Petrov-Galerkin projection to preserve structural features of interest, including…

Optimization and Control · Mathematics 2023-02-20 Xiaodong Cheng

We discuss the recent developments of projection-based model order reduction (MOR) techniques targeting Hamiltonian problems. Hamilton's principle completely characterizes many high-dimensional models in mathematical physics, resulting in…

Numerical Analysis · Mathematics 2021-09-28 J. S. Hesthaven , C. Pagliantini , N. Ripamonti

In time-limited model order reduction, a reduced-order approximation of the original high-order model is obtained that accurately approximates the original model within the desired limited time interval. Accuracy outside that time interval…

Systems and Control · Electrical Eng. & Systems 2022-12-19 Umair Zulfiqar , Xin Du , Qiuyan Song , Zhi-Hua Xiao , Victor Sreeram

In this paper, a computationally efficient frequency-limited model reduction algorithm is presented for large-scale interconnected power systems. The algorithm generates a reduced order model which not only preserves the electromechanical…

Systems and Control · Electrical Eng. & Systems 2020-01-28 Umair Zulfiqar , Victor Sreeram , Xin Du

This paper introduces an interpolation framework for the weighted-H2 model reduction problem. We obtain a new representation of the weighted-H2 norm of SISO systems that provides new interpolatory first order necessary conditions for an…

Numerical Analysis · Mathematics 2013-09-03 Branimir Anic , Christopher A. Beattie , Serkan Gugercin , Athanasios C. Antoulas

We present a novel data-driven reformulation of the iterative SVD-rational Krylov algorithm (ISRK), in its original formulation a Petrov-Galerkin (two-sided) projection-based iterative method for model reduction combining rational Krylov…

Numerical Analysis · Mathematics 2024-07-19 Ion Victor Gosea , Serkan Gugercin , Christopher Beattie

Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of…

Numerical Analysis · Mathematics 2024-09-23 Petar Mlinarić , Peter Benner , Serkan Gugercin