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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

We extend the modeling framework of port-Hamiltonian descriptor systems to include under- and over-determined systems and arbitrary differentiable Hamiltonian functions. This structure is associated with a Dirac structure that encloses its…

Optimization and Control · Mathematics 2019-03-26 Volker Mehrmann , Riccardo Morandin

We present a new balancing-based structure-preserving model reduction technique for linear port-Hamiltonian descriptor systems. The proposed method relies on a modification of a set of two dual generalized algebraic Riccati equations that…

Optimization and Control · Mathematics 2024-09-18 Tobias Breiten , Philipp Schulze

We present a new optimization-based structure-preserving model order reduction (MOR) method for port-Hamiltonian descriptor systems (pH-DAEs) with differentiation index two. Our method is based on a novel parameterization that allows us to…

Systems and Control · Electrical Eng. & Systems 2022-06-09 Tim Moser , Paul Schwerdtner , Volker Mehrmann , Matthias Voigt

Reduced basis methods are popular for approximately solving large and complex systems of differential equations. However, conventional reduced basis methods do not generally preserve conservation laws and symmetries of the full order model.…

Numerical Analysis · Mathematics 2018-03-20 Babak Maboudi Afkham , Jan S. Hesthaven

We investigate discretization strategies for a recently introduced class of energy-based models. The model class encompasses classical port-Hamiltonian systems, generalized gradient flows, and certain systems with algebraic constraints. Our…

Numerical Analysis · Mathematics 2026-05-29 Robert Altmann , Attila Karsai , Philipp Schulze

Interpolatory necessary optimality conditions for $\mathcal{H}_2$-optimal reduced-order modeling of unstructured linear time-invariant (LTI) systems are well-known. Based on previous work on $\mathcal{L}_2$-optimal reduced-order modeling of…

Numerical Analysis · Mathematics 2024-09-23 Petar Mlinarić , Peter Benner , Serkan Gugercin

With this contribution, we give a complete and comprehensive framework for modeling the dynamics of complex mechanical structures as port-Hamiltonian systems. This is motivated by research on the potential of lightweight construction using…

Computational Physics · Physics 2020-08-19 Alexander Warsewa , Michael Böhm , Oliver Sawodny , Cristina Tarín

Hamiltonian operator inference has been developed in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. The method…

Numerical Analysis · Mathematics 2025-07-21 Yuwei Geng , Lili Ju , Boris Kramer , Zhu Wang

In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order…

Numerical Analysis · Mathematics 2019-04-29 Peter Benner , Pawan Goyal

We present a new structure-preserving model order reduction (MOR) framework for large-scale port-Hamiltonian descriptor systems (pH-DAEs). Our method exploits the structural properties of the Rosenbrock system matrix for this system class…

Systems and Control · Electrical Eng. & Systems 2022-10-31 Tim Moser , Boris Lohmann

Direct numerical simulation of dynamical systems is of fundamental importance in studying a wide range of complex physical phenomena. However, the ever-increasing need for accuracy leads to extremely large-scale dynamical systems whose…

Dynamical Systems · Mathematics 2015-03-04 Jeff T. Borggaard , Serkan Gugercin

Suppressing vibrations in mechanical systems, usually described by second-order dynamical models, is a challenging task in mechanical engineering in terms of computational resources even nowadays. One remedy is structure-preserving model…

Optimization and Control · Mathematics 2023-09-25 Rebekka S. Beddig , Peter Benner , Ines Dorschky , Timo Reis , Paul Schwerdtner , Matthias Voigt , Steffen W. R. Werner

One approach to parametric and adaptive model reduction is via the interpolation of orthogonal bases, subspaces or positive definite system matrices. In all these cases, the sampled inputs stem from matrix sets that feature a geometric…

Numerical Analysis · Mathematics 2022-12-16 Ralf Zimmermann

We develop a structure-preserving parametric model reduction approach for linearized swing equations where parametrization corresponds to variations in operating conditions. We employ a global basis approach to develop the parametric…

Systems and Control · Electrical Eng. & Systems 2021-02-11 Bita Safaee , Serkan Gugercin

In this paper, we develop high-order splitting methods for linear port-Hamiltonian systems, focusing on preserving their intrinsic structure, particularly the dissipation inequality. Port-Hamiltonian systems are characterized by their…

Mathematical Physics · Physics 2024-09-16 Marius Mönch , Nicole Marheineke

We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…

Numerical Analysis · Mathematics 2021-04-05 Ion Victor Gosea , Serkan Gugercin , Benjamin Unger

This work proposes a hyper-reduction method for nonlinear parametric dynamical systems characterized by gradient fields such as Hamiltonian systems and gradient flows. The gradient structure is associated with conservation of invariants or…

Numerical Analysis · Mathematics 2023-07-24 Cecilia Pagliantini , Federico Vismara

Discrete gradient methods are a powerful tool for the time discretization of dynamical systems, since they are structure-preserving regardless of the form of the total energy. In this work, we discuss the application of discrete gradient…

Numerical Analysis · Mathematics 2026-01-06 Philipp L. Kinon , Riccardo Morandin , Philipp Schulze

Port-Hamiltonian systems have gained a lot of attention in recent years due to their inherent valuable properties in modeling and control. In this paper, we are interested in constructing linear port-Hamiltonian systems from time-domain…

Systems and Control · Electrical Eng. & Systems 2020-11-18 Karim Cherifi , Pawan Goyal , Peter Benner