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We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and…

Optimization and Control · Mathematics 2017-05-02 Peter Benner , Pawan Goyal

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

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 show that two widely accepted model reduction techniques, Balanced Truncation and Balanced Singular Perturbation Approximation, can be derived as limiting approximations of a carefully constructed parameterization of Linear Time…

Optimization and Control · Mathematics 2019-01-10 Philip E. Paré , David Grimsman , Alma T. Wilson , Mark K. Transtrum , Sean Warnick

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

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

A nonlinear MPC framework is presented that is suitable for dynamical systems with sampling times in the (sub)millisecond range and that allows for an efficient implementation on embedded hardware. The algorithm is based on an augmented…

Optimization and Control · Mathematics 2018-12-10 Tobias Englert , Andreas Völz , Felix Mesmer , Sönke Rhein , Knut Graichen

In this work, we present a nonlinear model reduction approach for reducing two commonly used nonlinear dynamical models of power grids: the effective network (EN) model and the synchronous motor (SM) model. Such models are essential in…

Systems and Control · Electrical Eng. & Systems 2020-05-27 Tobias K. S. Ritschel , Frances Weiß , Manuel Baumann , Sara Grundel

Version 5.99 of the empirical Gramian framework -- "emgr" -- completes a development cycle which focused on parametric model order reduction of gas network models while preserving compatibility to the previous development for the…

Computational Engineering, Finance, and Science · Computer Science 2022-09-09 Christian Himpe

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

Balanced truncation is a well-established model order reduction method which has been applied to a variety of problems. Recently, a connection between linear Gaussian Bayesian inference problems and the system-theoretic concept of balanced…

Numerical Analysis · Mathematics 2024-01-04 Josie König , Melina A. Freitag

In this paper, we consider model order reduction for bilinear systems with non-zero initial conditions. We discuss choices of Gramians for both the homogeneous and the inhomogeneous parts of the system individually and prove how these…

Numerical Analysis · Mathematics 2022-05-19 Martin Redmann , Igor Pontes Duff

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

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

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

Nonlinear grey system models, serving to time series forecasting, are extensively used in diverse areas of science and engineering. However, most research concerns improving classical models and developing novel models, relatively limited…

Applications · Statistics 2022-02-09 Lu Yang , Naiming Xie , Baolei Wei , Xiaolei Wang

What makes a class of quantum circuits efficiently classically simulable on average? I present a framework that applies harmonic analysis of groups to circuits with a structure encoded by group parameters. Expanding the circuits in a…

Quantum Physics · Physics 2024-10-18 Cristina Cirstoiu

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

In this paper, we present a toolbox for structured model reduction developed for MATLAB. In addition to structured model reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured…

Optimization and Control · Mathematics 2014-10-20 Martin Biel , Farhad Farokhi , Henrik Sandberg

In this paper, nonlinear model reduction for power systems is performed by the balancing of empirical controllability and observability covariances that are calculated around the operating region. Unlike existing model reduction methods,…

Systems and Control · Computer Science 2016-08-30 Junjian Qi , Jianhui Wang , Hui Liu , Aleksandar D. Dimitrovski