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Related papers: Discrete-time port-Hamiltonian systems: A definiti…

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The port-Hamiltonian framework is a structure-preserving modeling approach that preserves key physical properties such as energy conservation and dissipation. When subsystems are modeled as port-Hamiltonian systems (pHS) with linearly…

Dynamical Systems · Mathematics 2025-11-26 Matthias Ehrhardt , Michael Günther , Daniel Ševčovič

For a general class of nonlinear port-Hamiltonian systems we develop a high-order time discretization scheme with certain structure preservation properties. The finite or infinite-dimensional system under consideration possesses a…

Numerical Analysis · Mathematics 2024-07-23 Jan Giesselmann , Attila Karsai , Tabea Tscherpel

We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a…

Numerical Analysis · Mathematics 2026-04-14 Antoine Bendimerad-Hohl , Ghislain Haine , Laurent Lefèvre , Denis Matignon

This paper contributes with a new formal method of spatial discretization of a class of nonlinear distributed parameter systems that allow a port-Hamiltonian representation over a one dimensional manifold. A specific finite dimensional…

Numerical Analysis · Mathematics 2021-04-23 B. C. van Huijgevoort , S. Weiland , H. J. Zwart

This paper offers a geometric framework for modeling port-Hamiltonian systems on discrete manifolds. The simplicial Dirac structure, capturing the topological laws of the system, is defined in terms of primal and dual cochains related by…

Optimization and Control · Mathematics 2012-01-30 Marko Seslija , Jacquelien M. A. Scherpen , Arjan van der Schaft

We study the discretization of (almost-)Dirac structures using the notion of retraction and discretization maps on manifolds. Additionally, we apply the proposed discretization techniques to obtain numerical integrators for port-Hamiltonian…

Numerical Analysis · Mathematics 2025-05-12 María Barbero-Liñán , Juan Manuel López Medel , David Martín de Diego

Recently, continuous-time dynamical systems have proved useful in providing conceptual and quantitative insights into gradient-based optimization, widely used in modern machine learning and statistics. An important question that arises in…

Optimization and Control · Mathematics 2021-04-29 Guilherme França , Michael I. Jordan , René Vidal

Port-based network modeling of multi-physics problems leads naturally to a formulation as port-Hamiltonian differential-algebraic system. In this way, the physical properties are directly encoded in the structure of the model. Since the…

Optimization and Control · Mathematics 2024-12-20 Sarah-Alexa Hauschild , Nicole Marheineke , Volker Mehrmann

We consider the design of structure-preserving discretization methods for the solution of systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-Hamiltonian formalism. We first provide a novel general…

Numerical Analysis · Mathematics 2020-09-30 Andrea Brugnoli , Ghislain Haine , Anass Serhani , Xavier Vasseur

Hamiltonian systems are differential equations which describe systems in classical mechanics, plasma physics, and sampling problems. They exhibit many structural properties, such as a lack of attractors and the presence of conservation…

Numerical Analysis · Mathematics 2022-01-14 Christian Offen , Sina Ober-Blöbaum

This paper addresses the issue of structure-preserving discretization of open distributed-parameter systems with Hamiltonian dynamics. Employing the formalism of discrete exterior calculus, we introduce a simplicial Dirac structure as a…

Mathematical Physics · Physics 2012-02-28 Marko Seslija , Arjan van der Schaft , Jacquelien M. A. Scherpen

We present the mixed Galerkin discretization of distributed parameter port-Hamiltonian systems. On the prototypical example of hyperbolic systems of two conservation laws in arbitrary spatial dimension, we derive the main contributions: (i)…

Dynamical Systems · Mathematics 2018-03-02 Paul Kotyczka , Bernhard Maschke , Laurent Lefèvre

Port-Hamiltonian systems theory provides a systematic methodology for the modeling, simulation and control of multi-physics systems. The incorporation of algebraic constraints has led to a multitude of definitions of port-Hamiltonian…

Optimization and Control · Mathematics 2022-11-15 Arjan van der Schaft , Volker Mehrmann

Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…

Numerical Analysis · Mathematics 2023-10-10 Anand Srinivasan , Jose E. Castillo

This paper proposes to build a bridge between microscopic descriptions of matter with internal energy, composed of many fast interacting particles inside an environment, and their port-Hamiltonian (PH) descriptions at macroscopic scale. The…

Dynamical Systems · Mathematics 2023-01-16 Judy Najnudel , Thomas Hélie , David Roze , Rémy Muller

Methods for discretizing port-Hamiltonian systems are of interest both for simulation and control purposes. Despite the large literature on mixed finite elements, no rigorous analysis of the connections between mixed elements and…

Numerical Analysis · Mathematics 2020-06-09 Andrea Brugnoli , Daniel Alazard , Valérie Pommier-Budinger , Denis Matignon

We present a gradient-based identification algorithm to identify the system matrices of a linear port-Hamiltonian system from given input-output time data. Aiming for a direct structure-preserving approach, we employ techniques from optimal…

Optimization and Control · Mathematics 2023-12-22 Michael Günther , Birgit Jacob , Claudia Totzeck

In this paper we present a unifying geometric and compositional framework for modeling complex physical network dynamics as port-Hamiltonian systems on open graphs. Basic idea is to associate with the incidence matrix of the graph a Dirac…

Optimization and Control · Mathematics 2012-09-07 A. J. van der Schaft , B. M. Maschke

We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the…

Dynamical Systems · Mathematics 2023-02-13 Riccardo Morandin , Jonas Nicodemus , Benjamin Unger

The high volatility of renewable energies calls for more energy efficiency. Thus, different physical systems need to be coupled efficiently although they run on various time scales. Here, the port-Hamiltonian (pH) modeling framework comes…

Numerical Analysis · Mathematics 2024-04-09 Sarah-Alexa Hauschild , Nicole Marheineke