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Related papers: Data-driven balancing of linear dynamical systems

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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

In this paper, we present a theoretical analysis of the model reduction algorithm for linear switched systems. This algorithm is a reminiscence of the balanced truncation method for linear parameter varying systems. Specifically in this…

Optimization and Control · Mathematics 2013-03-19 Mihaly Petreczky , Rafael Wisniewski , John Leth

We present a framework for constructing a structured realization of a linear time-invariant dynamical system solely from a discrete sampling of an input and output trajectory of the system. We estimate the transfer function of the original…

Optimization and Control · Mathematics 2019-02-15 Elliot Fosong , Philipp Schulze , Benjamin Unger

Model order reduction involves constructing a reduced-order approximation of a high-order model while retaining its essential characteristics. This reduced-order model serves as a substitute for the original one in various applications such…

Systems and Control · Electrical Eng. & Systems 2024-03-06 Qiu-Yan Song , Umair Zulfiqar , Zhi-Hua Xiao , Mohammad Monir Uddin , Victor Sreeram

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 introduce a data-driven modeling approach for dynamics problems with latent variables. The state-space of the proposed model includes artificial latent variables, in addition to observed variables that can be fitted to a…

Optimization and Control · Mathematics 2024-06-19 Yushuang Luo , Xiantao Li , Wenrui Hao

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

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 propose a model order reduction approach for balanced truncation of linear switched systems. Such systems switch among a finite number of linear subsystems or modes. We compute pairs of controllability and observability Gramians…

Numerical Analysis · Mathematics 2017-12-07 Ion Victor Gosea , Mihaly Petreczky , Athanasios C. Antoulas , Christophe Fiter

Model reduction is a powerful tool in dealing with numerical simulation of large scale dynamic systems for studying complex physical systems. Two major types of model reduction methods for linear time-invariant dynamic systems are Krylov…

Numerical Analysis · Mathematics 2024-06-11 Lei-Hong Zhang , Ren-Cang Li

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

To implement deep learning models on edge devices, model compression methods have been widely recognized as useful. However, it remains unclear which model compression methods are effective for Structured State Space Sequence (S4) models…

Machine Learning · Computer Science 2024-07-02 Haruka Ezoe , Kazuhiro Sato

In this contribution, we propose a data-driven procedure to fit quadratic-bilinear surrogate models from data. Although the dynamics characterizing the original model are strongly nonlinear, we rely on lifting techniques to embed the…

Systems and Control · Electrical Eng. & Systems 2021-12-03 Dimitrios S. Karachalios , Ion Victor Gosea , Athanasios C. Antoulas

In this paper, we address an extension of the Loewner framework for learning quadratic control systems from input-output data. The proposed method first constructs a reduced-order linear model from measurements of the classical transfer…

Optimization and Control · Mathematics 2020-12-04 Ion Victor Gosea , Dimitrios S. Karachalios , Athanasios C. Antoulas

Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales.…

Chaotic Dynamics · Physics 2025-10-06 Chenyu Dong , Davide Faranda , Adriano Gualandi , Valerio Lucarini , Gianmarco Mengaldo

Model order reduction algorithms for large-scale descriptor systems are proposed using balanced truncation, in which symmetry or block skew symmetry (reciprocity) and the positive realness of the original transfer matrix are preserved. Two…

Numerical Analysis · Computer Science 2018-11-13 Yuichi Tanji

Balanced truncation (BT) is a model reduction method that utilizes a coordinate transformation to retain eigen-directions that are highly observable and reachable. To address realizability and scalability of BT applied to highly stiff and…

Systems and Control · Electrical Eng. & Systems 2022-07-13 Elnaz Rezaian , Cheng Huang , Karthik Duraisamy

This paper introduces a quadrature-free, non-intrusive approach to balanced truncation for both continuous-time and discrete-time systems. The method non-intrusively constructs reduced-order models using available transfer function samples…

Systems and Control · Electrical Eng. & Systems 2026-02-20 Umair Zulfiqar

This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated…

Fluid Dynamics · Physics 2026-04-15 Brandon Choi , Matteo Ugliotti , Mateo Reynoso , Daniel R. Gurevich , Roman O. Grigoriev