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Related papers: Empirical balanced truncation of nonlinear systems

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This paper presents a novel model order reduction framework tailored for fully nonlinear stochastic dynamics without lifting them to quadratic systems and without using linearization techniques. By directly leveraging structural properties…

Probability · Mathematics 2025-08-05 Martin Redmann

We deduce a procedure to apply balanced truncation to parameter-dependent differential-algebraic systems. For that we solve multiple projected Lyapunov equations for different parameter values to compute the Gramians that are required for…

Dynamical Systems · Mathematics 2024-01-08 Jennifer Przybilla , Matthias Voigt

We consider the problem of constructing reduced models for large scale systems with poles in general domains in the complex plane (as opposed to, e.g., the open left-half plane or the open unit disk). Our goal is to design a model reduction…

Numerical Analysis · Mathematics 2025-02-10 Alessandro Borghi , Tobias Breiten , Serkan Gugercin

We develop the framework for a non-intrusive, quadrature-based method for approximate balanced truncation (QuadBT) of linear systems with quadratic outputs, thus extending the applicability of QuadBT, which was originally designed for…

Numerical Analysis · Mathematics 2025-09-17 Reetish Padhi , Ion Victor Gosea , Igor Pontes Duff , Serkan Gugercin

This paper studies model order reduction of multi-agent systems consisting of identical linear passive subsystems, where the interconnection topology is characterized by an undirected weighted graph. Balanced truncation based on a pair of…

Optimization and Control · Mathematics 2019-01-29 Xiaodong Cheng , Jacquelien M. A. Scherpen , Bart Besselink

Quadrature-based approximation of Gramians in standard balanced truncation yields a non-intrusive, data-driven implementation that requires only transfer function samples on the imaginary axis, which can be measured experimentally. This…

Systems and Control · Electrical Eng. & Systems 2026-03-24 Umair Zulfiqar , Qiu-Yan Song , Zhi-Hua Xiao , Victor Sreeram

This paper deals with the balanced truncation model reduction of discrete-time, linear time-varying, heterogeneous subsystems interconnected over finite arbitrary directed graphs. The information transfer between the subsystems is subject…

Optimization and Control · Mathematics 2017-08-15 Dany Abou Jaoude , Mazen Farhood

Reduced-order models for flows that exhibit time-periodic behavior are critical for several tasks, including active control and optimization. One well-known procedure to obtain the desired reduced-order model in the proximity of a periodic…

Fluid Dynamics · Physics 2022-08-30 Alberto Padovan , Clarence W. Rowley

This paper concerns the recently proposed quasi-balanced truncation model reduction method for linear quantum stochastic systems. It has previously been shown that the quasi-balanceable class of systems (i.e. systems that can be truncated…

Quantum Physics · Physics 2014-08-11 Onvaree Techakesari , Hendra I. Nurdin

The theory of nonlinear balanced truncation provides a system-theoretic framework for model reduction that preserves important properties such as stability, controllability, and observability. We present a scalable algorithm for computing…

Optimization and Control · Mathematics 2026-04-28 Nicholas A. Corbin , Boris Kramer

When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…

Numerical Analysis · Mathematics 2020-03-11 Nguyen Thanh Son , Pierre-Yves Gousenbourger , Estelle Massart , Tatjana Stykel

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 this paper, we consider a model reduction technique for stabilizable and detectable stochastic systems. It is based on a pair of Gramians that we analyze in terms of well-posedness. Subsequently, dominant subspaces of the stochastic…

Optimization and Control · Mathematics 2023-11-07 Tobias Damm , Martin Redmann

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

In this work, the empirical-Gramian-based model reduction methods: Empirical poor man's truncated balanced realization, empirical approximate balancing, empirical dominant subspaces, empirical balanced truncation, and empirical balanced…

Optimization and Control · Mathematics 2020-02-28 Christian Himpe

This paper studies the data-driven balanced truncation (BT) method for second-order systems based on the measurements in the frequency domain. The basic idea is to approximate Gramians used the numerical quadrature rules, and establish the…

Numerical Analysis · Mathematics 2025-06-05 Xiaolong Wang , Xuerong Yang , Xiaoli Wang , Bo Song

The cross gramian matrix is a tool for model reduction and system identification, but it is only computable for square control systems. For symmetric systems the cross gramian possesses a useful relation to the system's associated Hankel…

Optimization and Control · Mathematics 2016-08-22 Christian Himpe , Mario Ohlberger

We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on…

Optimization and Control · Mathematics 2009-03-03 John M. Davis , Ian A. Gravagne , Billy J. Jackson , Robert J. Marks

Recent years have witnessed a wave of research activities in systems science toward the study of population systems. The driving force behind this shift was geared by numerous emerging and ever-changing technologies in life and physical…

Optimization and Control · Mathematics 2019-08-16 Jr-Shin Li , Wei Zhang , Lin Tie

As a special type of bilinear systems, K-power bilinear systems possess a special coupled structure along with nice properties in practice. In this paper, we investigate the data-driven counterpart of balanced truncation for K-power…

Optimization and Control · Mathematics 2026-04-14 Xiaolong Wang , Biaolin Li , Xiaoli Wang