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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 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 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

We propose a control approach for a class of nonlinear mechanical systems to stabilize the system under study while ensuring that the oscillations of the transient response are reduced. The approach is twofold: (i) we apply our technique…

Systems and Control · Electrical Eng. & Systems 2022-06-22 Carmen Chan-Zheng , Pablo Borja , Jacquelien Scherpen

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

Dynamical systems can be used to model a broad class of physical processes, and conservation laws give rise to system properties like passivity or port-Hamiltonian structure. An important problem in practical applications is to steer…

Optimization and Control · Mathematics 2025-10-29 Tobias Breiten , Attila Karsai

Model order reduction plays a crucial role in simplifying complex systems while preserving their essential dynamic characteristics, making it an invaluable tool in a wide range of applications, including robotic systems, signal processing,…

Systems and Control · Electrical Eng. & Systems 2025-04-22 Shenghan Mei , Ziqin He , Yidan Mei , Xin Mao , Anqi Dong , Ren Wang , Can Chen

In this paper, we investigate a large-scale stochastic system with bilinear drift and linear diffusion term. Such high dimensional systems appear for example when discretizing a stochastic partial differential equations in space. We study a…

Optimization and Control · Mathematics 2018-04-06 Martin Redmann

In this paper, we explore the role of tensor algebra in balanced truncation (BT) based model reduction/identification for high-dimensional multilinear/linear time invariant systems. In particular, we employ tensor train decomposition (TTD),…

Systems and Control · Electrical Eng. & Systems 2020-01-28 Can Chen , Amit Surana , Anthony Bloch , Indika Rajapakse

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

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

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

Positive systems naturally arise in situations where the model tracks physical quantities. Although the linear case is well understood, analysis and controller design for nonlinear positive systems remain challenging. Model reduction…

Optimization and Control · Mathematics 2023-12-15 Antonio Jiménez-Pastor , Daniele Toller , Mirco Tribastone , Max Tschaikowski , Andrea Vandin

Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…

Systems and Control · Electrical Eng. & Systems 2020-11-30 Michael Ruderman

In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…

Numerical Analysis · Mathematics 2024-08-29 Hendrik Kleikamp , Lukas Renelt

Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…

Optimization and Control · Mathematics 2019-09-11 Peter Benner , Pawan Goyal , Igor Pontes Duff

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

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 treat extended balancing for continuous-time linear time-invariant systems, and we address the problem of structure-preserving model reduction of the subclass of port-Hamiltonian systems. We establish sufficient conditions…

Systems and Control · Electrical Eng. & Systems 2020-01-06 Pablo Borja , Jacquelien M. A. Scherpen , Kenji Fujimoto

This manuscript describes several approaches to tune the parameters of a class of passivity-based controllers for standard nonlinear mechanical systems. In particular, we are interested in controllers that preserve the mechanical system…

Systems and Control · Electrical Eng. & Systems 2023-02-20 Carmen Chan-Zheng , Pablo Borja , Jacquelien M. A. Scherpen