English
Related papers

Related papers: Balanced Truncation of Networked Linear Passive Sy…

200 papers

Reduced-order modeling techniques, including balanced truncation and $\mathcal{H}_2$-optimal model reduction, exploit the structure of linear dynamical systems to produce models that accurately capture the dynamics. For nonlinear systems…

Optimization and Control · Mathematics 2022-01-17 Samuel E. Otto , Alberto Padovan , Clarence W. Rowley

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

Novel constructions of empirical controllability and observability gramians for nonlinear systems for subsequent use in a balanced truncation style of model reduction are proposed. The new gramians are based on a generalisation of the…

Optimization and Control · Mathematics 2007-05-23 Marissa Condon , Rossen I. Ivanov

This paper proposes a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin…

Optimization and Control · Mathematics 2022-02-01 Azka Muji Burohman , Bart Besselink , Jacquelien M. A. Scherpen , M. Kanat Camlibel

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

The purpose of this paper is to develop a model reduction theory for linear quantum stochastic systems that are commonly encountered in quantum optics and related fields, modeling devices such as optical cavities and optical parametric…

Quantum Physics · Physics 2013-08-29 Hendra I. Nurdin

We consider two approaches to balanced truncation of stochastic linear systems, which follow from different generalizations of the reachability Gramian of deterministic systems. Both preserve mean-square asymptotic stability, but only the…

Dynamical Systems · Mathematics 2017-03-14 Peter Benner , Tobias Damm , Yolanda Rocio Rodriguez Cruz

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

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

This work discusses model reduction for differential-algebraic systems with quadratic output equations. Under mild conditions, these systems can be transformed into a Weierstra{\ss} canonical form and, thus, be decoupled into differential…

Dynamical Systems · Mathematics 2024-02-23 Jennifer Przybilla , Igor Pontes Duff , Pawan Goyal , Peter Benner

Nonlinear balanced truncation is a model order reduction technique that reduces the dimension of nonlinear systems in a manner that accounts for either open- or closed-loop observability and controllability aspects of the system. Two…

Optimization and Control · Mathematics 2023-02-07 Boris Kramer , Serkan Gugercin , Jeff Borggaard

We present a balanced truncation model reduction approach for a class of nonlinear systems with time-varying and uncertain inputs. First, our approach brings the nonlinear system into quadratic-bilinear~(QB) form via a process called…

Numerical Analysis · Mathematics 2020-10-29 Boris Kramer , Karen E. Willcox

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

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

We consider linear magneto-quasistatic field equations which arise in simulation of low-frequency electromagnetic devices coupled to electrical circuits. A finite element discretization of such equations on 3D domains leads to a singular…

Numerical Analysis · Mathematics 2019-11-21 Johanna Kerler-Back , Tatjana Stykel

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…

Numerical Analysis · Mathematics 2026-05-25 Sean Reiter , Steffen W. R. Werner

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

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

The paper presents a model reduction framework geared towards the analysis and design of systems that switch and oscillate. While such phenomena are ubiquitous in nature and engineering, model reduction methods are not well developed for…

Systems and Control · Electrical Eng. & Systems 2020-05-19 Alberto Padoan , Fulvio Forni , Rodolphe Sepulchre

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