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In this article, we show that the projection-free, snapshot-based, balanced truncation method can be applied directly to unstable systems. We prove that even for unstable systems, the unmodified balanced proper orthogonal decomposition…

Fluid Dynamics · Physics 2015-08-27 Thibault L. B. Flinois , Aimee S. Morgans , Peter J. Schmid

The aim in model order reduction is to approximate an input-output map described by a large-scale dynamical system with a low-dimensional and cheaper-to-evaluate reduced order model. While high fidelity can be achieved by a variety of…

Dynamical Systems · Mathematics 2023-01-04 Björn Liljegren-Sailer

We analyze a structure-preserving model order reduction technique for delay and stochastic delay equations based on the balanced truncation method and provide a system theoretic interpretation. Transferring error bounds based on Hankel…

Optimization and Control · Mathematics 2020-08-28 Simon Becker , Lorenz Richter

When solving partial differential equations numerically, usually a high order spatial discretisation is needed. Model order reduction (MOR) techniques are often used to reduce the order of spatially-discretised systems and hence reduce…

Optimization and Control · Mathematics 2017-09-19 Martin Redmann

We present a novel reformulation of balanced truncation, a classical model reduction method. The principal innovation that we introduce comes through the use of system response data that has been either measured or computed, without…

Numerical Analysis · Mathematics 2021-10-26 Ion Victor Gosea , Serkan Gugercin , Christopher Beattie

This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by Hankel matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has order $k$ or less,…

Optimization and Control · Mathematics 2022-02-17 Christian Grussler , Tobias Damm , Rodolphe Sepulchre

A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system. The related dominant subspace projection model…

Optimization and Control · Mathematics 2019-08-23 Peter Benner , Christian Himpe

Model order reduction (MOR) is often applied to spatially-discretized partial differential equations to reduce their order and hence decrease computational complexity. A reduced system can be obtained, e.g., by time-limited balanced…

Optimization and Control · Mathematics 2019-07-15 Martin Redmann

We investigate model order reduction (MOR) for linear dynamical systems, where a quadratic output is defined as a quantity of interest. The system can be transformed into a linear dynamical system with many linear outputs. MOR is feasible…

Numerical Analysis · Mathematics 2019-08-15 Roland Pulch , Akil Narayan

This paper discusses model order reduction of LTI systems over limited frequency intervals within the framework of balanced truncation. Two new \emph{frequency-dependent balanced truncation} methods were developed, one is \emph{SF-type…

Systems and Control · Computer Science 2016-02-16 Xin Du , Peter Benner

Balanced truncation, a technique from robust control theory, is a systematic method for producing simple approximate models of complex linear systems. This technique may have significant applications in physics, particularly in the study of…

Quantum Physics · Physics 2007-05-23 Benjamin Rahn

In standard balanced truncation model order reduction, the initial condition is typically ignored in the reduction procedure and is assumed to be zero instead. However, such a reduced-order model may be a bad approximation to the full-order…

Systems and Control · Electrical Eng. & Systems 2022-03-16 Christian Schröder , Matthias Voigt

We introduce an algorithm based on a method of snapshots for computing approximate balanced truncations for discrete-time, stable, linear time-periodic systems. By construction, this algorithm is applicable to very high-dimensional systems,…

Optimization and Control · Mathematics 2007-08-06 Zhanhua Ma , Clarence W. Rowley , Gilead Tadmor

We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at…

Optimization and Control · Mathematics 2018-11-27 Belinda A. Batten , Hesam Shoori , John R. Singler , Madhuka H. Weerasinghe

In this paper, we consider the problem of finding surrogate models for large-scale second-order linear time-invariant systems with inhomogeneous initial conditions. For this class of systems, the superposition principle allows us to…

Dynamical Systems · Mathematics 2022-06-24 Jennifer Przybilla , Igor Pontes Duff , Peter Benner

In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…

Numerical Analysis · Mathematics 2019-02-06 Igor Pontes Duff , Patrick Kürschner

This paper proposes a balancing-based model reduction approach for an interconnection of passive dynamic subsystems. This approach preserves the passivity and stability of both the subsystems and the interconnected system. Hereto, one…

Systems and Control · Electrical Eng. & Systems 2023-11-23 Luuk Poort , Bart Besselink , Rob H. B. Fey , Nathan van de Wouw

Balanced truncation is one of the most common model order reduction schemes. In this paper, we study finite-frequency model order reduction (FF-MOR) problems of linear continuous-time systems within the framework of balanced truncation…

Systems and Control · Computer Science 2017-03-21 Xin Du , Peter Benner

We consider a class of finite element approximations for fourth-order parabolic equations that can be written as a system of second-order equations by introducing an auxiliary variable. In our approach, we first solve a variational problem…

Numerical Analysis · Mathematics 2021-06-30 Sana Keita , Abdelaziz Beljadid , Yves Bourgault

We propose two kinds of model order reduction methods for discrete time-delay systems with inhomogeneous initial conditions. The peculiar properties of discrete Walsh functions are directly utilized to compute the Walsh coefficients of the…

Optimization and Control · Mathematics 2024-06-07 Xiaolong Wang , Kejia Xu