English
Related papers

Related papers: Commutator-based operator splitting for linear por…

200 papers

We study nonlinear singular optimal control problems of port-Hamil-tonian (descriptor) systems. We employ general control-affine cost functionals that include as a special case the energy supplied to the system. We first derive optimality…

Optimization and Control · Mathematics 2025-11-27 M. Soledad Aronna , Volker Mehrmann

Operator-splitting methods are widely used to solve differential equations, especially those that arise from multi-scale or multi-physics models, because a monolithic (single-method) approach may be inefficient or even infeasible. The most…

Numerical Analysis · Mathematics 2025-01-07 Siqi Wei , Victoria Guenter , Raymond J. Spiteri

In this article we study port-Hamiltonian partial differential equations on certain one-dimensional manifolds. We classify those boundary conditions that give rise to contraction semigroups. As an application we study port-Hamiltonian…

Functional Analysis · Mathematics 2021-11-09 Marcus Waurick , Sven-Ake Wegner

While symplectic integration methods based on operator splitting are well established in many branches of science, high order methods for Hamiltonian systems that split in more than two parts have not been studied in great detail. Here, we…

Computational Physics · Physics 2015-06-15 Ch. Skokos , E. Gerlach , J. D. Bodyfelt , G. Papamikos , S. Eggl

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

Given an energy-dissipating port-Hamiltonian system, we characterise the exponential decay of the energy via the model ingredients under mild conditions on the Hamiltonian density $\mathcal{H}$. In passing, we obtain generalisations for…

Analysis of PDEs · Mathematics 2024-02-29 Sascha Trostorff , Marcus Waurick

This work proposes a suite of numerical techniques to facilitate the design of structure-preserving integrators for nonlinear dynamics. The celebrated LaBudde-Greenspan integrator and various energy-momentum schemes adopt a difference…

Numerical Analysis · Mathematics 2023-05-17 Ju Liu

We propose a hierarchical splitting approach to differential equations that provides a design principle for constructing splitting methods for $N$-split systems by iteratively applying splitting methods for two-split systems. We analyze the…

Numerical Analysis · Mathematics 2026-01-21 Kevin Schäfers , Michael Günther

The relationship between different dissipativity concepts for linear time-varying systems is studied, in particular between port-Hamiltonian systems, passive systems, and systems with nonnegative supply. It is shown that linear time-varying…

Optimization and Control · Mathematics 2024-12-24 Karim Cherifi , Hannes Gernandt , Dorothea Hinsen , Volker Mehrmann , Riccardo Morandin

It is well known that any port-Hamiltonian (pH) system is passive, and conversely, any minimal and stable passive system has a pH representation. Nevertheless, this equivalence is only concerned with the input-output mapping but not with…

Optimization and Control · Mathematics 2025-03-12 Tobias Holicki , Jonas Nicodemus , Paul Schwerdtner , Benjamin Unger

We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems subject to control and terminal state constraints. To this end, after reducing the problem to an ODE…

Optimization and Control · Mathematics 2022-02-16 Timm Faulwasser , Bernhard Maschke , Friedrich Philipp , Manuel Schaller , Karl Worthmann

This article presents a systematic methodology for modeling a class of flexible multidimensional mechanical structures defined by linear elastic relations that directly allows to obtain their infinite-dimensional port-Hamiltonian…

Dynamical Systems · Mathematics 2023-11-08 Cristobal Ponce , Yongxin Wu , Yann Le Gorrec , Hector Ramirez

In this work, the multiplier method is extended to obtain a general lower bound of the exponential decay rate in terms of the physical parameters for port-Hamiltonian systems in one space dimension with boundary dissipation. The physical…

Analysis of PDEs · Mathematics 2023-03-17 Luis A. Mora , Kirsten Morris

Port-Hamiltonian systems provide a highly-structured framework for modeling of physical systems. By definition, they encode a balance equation relating energy changes to supplied and dissipated energy. Capturing this energy balance in…

Numerical Analysis · Mathematics 2026-05-15 Aashutosh Sharma , Andreas Bartel , Manuel Schaller

Port-Hamiltonian systems provide an energy-based modeling paradigm for dynamical input-state-output systems. At their core, they fulfill an energy balance relating stored, dissipated and supplied energy. To accurately resolve this energy…

Numerical Analysis · Mathematics 2024-12-17 Andreas Bartel , Manuel Schaller

In this letter, we study the energy-optimal control of nonlinear port-Hamiltonian (pH) systems in discrete time. For continuous-time pH systems, energy-optimal control problems are strictly dissipative by design. This property, stating that…

Systems and Control · Electrical Eng. & Systems 2025-09-03 Arijit Sarkar , Vaibhav Kumar Singh , Manuel Schaller , Karl Worthmann

We consider Hamiltonian PDEs that can be split into a linear unbounded operator and a regular non linear part. We consider abstract splitting methods associated with this decomposition where no discretization in space is made. We prove a…

Numerical Analysis · Mathematics 2008-11-26 Erwan Faou , Benoit Grebert , Eric Paturel

Splitting methods constitute a widely used class of numerical integrators for ordinary and partial differential equations, particularly well suited to problems that can be decomposed into simpler subproblems. High-order splitting schemes…

Numerical Analysis · Mathematics 2026-04-02 Fernando Casas , Ander Murua

A rigid body model for the dynamics of a marine vessel, used in simulations of offshore pipe-lay operations, gives rise to a set of ordinary differential equations with controls. The system is input-output passive. We propose…

Numerical Analysis · Mathematics 2018-04-24 Elena Celledoni , Eirik Hoel Høiseth , Nataliya Ramzina

We develop optimization-based structure-preserving model order reduction (MOR) methods for port-Hamiltonian (pH) descriptor systems of differentiation index one. Descriptor systems in pH form permit energy-based modeling and intuitive…

Optimization and Control · Mathematics 2022-06-06 Paul Schwerdtner , Tim Moser , Volker Mehrmann , Matthias Voigt