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In this note, we consider port-Hamiltonian structures in numerical optimal control of ordinary differential equations. By introducing a novel class of nonlinear monotone port-Hamiltonian (pH) systems, we show that the primal-dual gradient…

Optimization and Control · Mathematics 2024-12-17 Hannes Gernandt , Manuel Schaller

Motivated by recent work in this area we expand on a generalization of port-Hamiltonian systems that is obtained by replacing the Hamiltonian function representing energy storage by a general Lagrangian subspace. This leads to a new class…

Optimization and Control · Mathematics 2018-08-07 Arjan van der Schaft , Bernhard Maschke

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

Port-Hamiltonian (PH) systems provide a framework for modeling, analysis and control of complex dynamical systems, where the complexity might result from multi-physical couplings, non-trivial domains and diverse nonlinearities. A major…

Dynamical Systems · Mathematics 2024-03-15 Philipp L. Kinon , Tobias Thoma , Peter Betsch , Paul Kotyczka

Port-Hamiltonian systems theory provides a structured approach to modelling, optimization and control of multiphysical systems. Yet, its relationship to thermodynamics seems to be unclear. The Hamiltonian is traditionally thought of as…

Classical Physics · Physics 2021-11-01 Markus Lohmayer , Paul Kotyczka , Sigrid Leyendecker

This paper focuses on the port-Hamiltonian formulation of systems described by partial differential equations. Based on a variational principle we derive the equations of motion as well as the boundary conditions in the well-known…

Optimization and Control · Mathematics 2021-07-29 Markus Schöberl , Andreas Siuka

Dirac structures are geometric objects that generalize both Poisson structures and presymplectic structures on manifolds. They naturally appear in the formulation of constrained mechanical systems. In this paper, we show that the evolution…

Mathematical Physics · Physics 2018-02-14 François Gay-Balmaz , Hiroaki Yoshimura

In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variables we will show how several elements coming from possibly…

Probability · Mathematics 2022-05-12 Francesco Cordoni , Luca Di Persio , Riccardo Muradore

A description of Lagrangian and Hamiltonian formalisms naturally arisen from the invariance structure of given nonlinear dynamical systems on the infinite--dimensional functional manifold is presented. The basic ideas used to formulate the…

Symplectic Geometry · Mathematics 2007-05-23 Yarema A. Prykarpatsky , Anatoliy M. Samoilenko

This work is devoted to the establishment of a Poisson structure for a format of equations known as Generalized Lotka-Volterra systems. These equations, which include the classical Lotka-Volterra systems as a particular case, have been…

Mathematical Physics · Physics 2019-11-01 Benito Hernández-Bermejo , Victor Fairén

Different representations of dissipative Hamiltonian and port-Hamiltonian differential-algebraic equations (DAE) systems are presented and compared. Using global geometric and algebraic points of view, translations between the different…

Optimization and Control · Mathematics 2023-02-10 V. Mehrmann , A. J. van der Schaft

Potential algebras can be used effectively in the analysis of the quantum systems. In the article, we focus on the systems described by a separable, 2x2 matrix Hamiltonian of the first order in derivatives. We find integrals of motion of…

Mathematical Physics · Physics 2015-06-11 Vit Jakubsky

In this paper we design discrete port-Hamiltonian systems systematically in two different ways, by applying discrete gradient methods and splitting methods respectively. The discrete port-Hamiltonian systems we get satisfy a discrete notion…

Numerical Analysis · Mathematics 2017-06-28 Elena Celledoni , Eirik Hoel Høiseth

We provide a generalization of the notion of Dirac system by using Morse families to intrinsically embrace the dynamics associated with different physical systems such as constrained variational calculus, optimal control, Lagrangian…

Mathematical Physics · Physics 2018-04-17 M. Barbero-Liñán , H. Cendra , E. García-Toraño Andrés , D. Martín de Diego

After recalling standard nonlinear port-Hamiltonian systems and their algebraic constraint equations, called here Dirac algebraic constraints, an extended class of port-Hamiltonian systems is introduced. This is based on replacing the…

Optimization and Control · Mathematics 2019-09-17 Arjan van der Schaft , Bernhard Maschke

The mechanical model of a thin plate with boundary control and observation is presented as a port-Hamiltonian system (pHs), both in vectorial and tensorial forms: the Kirchhoff-Love model of a plate is described by using a Stokes-Dirac…

Analysis of PDEs · Mathematics 2020-10-07 Andrea Brugnoli , Daniel Alazard , Valérie Pommier-Budinger , Denis Matignon

Electric circuits are usually described by charge- and flux-oriented modified nodal analysis. In this paper, we derive models as port-Hamiltonian systems on several levels: overall systems, multiply coupled systems and systems within…

Numerical Analysis · Mathematics 2020-04-28 Michael Günther , Andreas Bartel , Birgit Jacob , Timo Reis

The purpose of this paper is to define the concept of multi-Dirac structures and to describe their role in the description of classical field theories. We begin by outlining a variational principle for field theories, referred to as the…

Mathematical Physics · Physics 2010-10-22 Joris Vankerschaver , Hiroaki Yoshimura , Jerrold E. Marsden

We analyze infinite-dimensional Hamiltonian systems corresponding to partial differential equations on one-dimensional spatial domains formulated with formally skew-adjoint Hamiltonian operators and nonlinear Hamiltonian density. In various…

Analysis of PDEs · Mathematics 2024-01-30 Till Preuster , Manuel Schaller , Bernhard Maschke

The concept of a Dirac algebroid, which is a linear almost Dirac structure on a vector bundle, was designed to generate phase equations for mechanical systems with linear nonholonomic constraints. We apply it to systems with magnetic-like…

Mathematical Physics · Physics 2025-05-01 Katarzyna Grabowska , Michalina Borczyńska , Joanna Majsak , Tomasz Sobczak