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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

In this paper we propose a novel approach to discretize linear port-Hamiltonian systems while preserving the underlying structure. We present a finite element exterior calculus formulation that is able to mimetically represent conservation…

Numerical Analysis · Mathematics 2022-10-19 Andrea Brugnoli , Ramy Rashad , Stefano Stramigioli

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

Part I of this paper presented a systematic derivation of the Stokes Dirac structure underlying the port-Hamiltonian model of ideal fluid flow on Riemannian manifolds. Starting from the group of diffeomorphisms as a configuration space for…

Fluid Dynamics · Physics 2021-05-05 Ramy Rashad , Federico Califano , Frederic P. Schuller , Stefano Stramigioli

A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a list of consistency criteria with the geometric setting of…

Symplectic Geometry · Mathematics 2025-11-11 François Gay-Balmaz , Álvaro Rodríguez Abella , Hiroaki Yoshimura

We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes by Staffans to formulate a~suitable concept for port-Hamiltonian systems, which allows a…

Analysis of PDEs · Mathematics 2023-02-13 Friedrich Philipp , Timo Reis , Manuel Schaller

Correlated with the trend of increasing degrees of freedom in robotic systems is a similar trend of rising interest in Spatio-Temporal systems described by Partial Differential Equations (PDEs) among the robotics and control communities.…

Robotics · Computer Science 2021-02-19 Ethan N. Evans , Andrew P. Kendall , Evangelos A. Theodorou

PDE-constrained optimization is a field of numerical analysis that combines the theory of PDEs, nonlinear optimization and numerical linear algebra. Optimization problems of this kind arise in many physical applications, prominently in…

Numerical Analysis · Mathematics 2017-10-18 Gennadij Heidel , Andy Wathen

We consider a control problem constrained by the unsteady stochastic Stokes equations with nonhomogeneous boundary conditions in connected and bounded domains. In this paper, controls are defined inside the domain as well as on the…

Optimization and Control · Mathematics 2018-09-05 Peter Benner , Christoph Trautwein

In this paper we present a novel approach to the geometric formulation of solid and fluid mechanics within the port-Hamiltonian framework, which extends the standard Hamiltonian formulation to non-conservative and open dynamical systems.…

Mathematical Physics · Physics 2024-04-19 Ramy Rashad , Stefano Stramigioli

Although conservative Hamiltonian systems with constraints can be formulated in terms of Dirac structures, a more general framework is necessary to cover also dissipative systems such as gradient and metriplectic systems with constraints.…

Differential Geometry · Mathematics 2013-03-05 Ünver Çiftçi

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

We extend the port-Hamiltonian framework defined with respect to a Lagrangian submanifold and a Dirac structure by augmenting the Lagrangian submanifold with the space of external variables. The new pair of conjugated variables is called…

Optimization and Control · Mathematics 2024-05-03 Kaja Krhac , Bernhard Maschke , Arjan van der Schaft

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

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

We extend deterministic port-Hamiltonian systems (PHS) to a stochastic framework by means of stochastic differential equations. As the dissipation inequality plays a crucial role for deterministic PHS, we develop several passivity concepts…

Optimization and Control · Mathematics 2025-12-08 Julia Ackermann , Thomas Kruse , Stefan Tappe

The modeling framework of port-Hamiltonian descriptor systems and their use in numerical simulation and control are discussed. The structure is ideal for automated network-based modeling since it is invariant under power-conserving…

Dynamical Systems · Mathematics 2022-01-19 Volker Mehrmann , Benjamin Unger

Control theory often takes the mathematical model of the to-be-control-led system for granted. In contrast, port-Hamiltonian systems theory bridges the gap between modelling and control for physical systems. It provides a unified framework…

Optimization and Control · Mathematics 2024-12-30 Arjan van der Schaft

The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…

Optimization and Control · Mathematics 2022-05-03 Cornel Marius Murea , Dan Tiba

In this paper, we propose a novel algebraic and geometric description for the dissipative dynamics. Our formulation bears some similarity to the Poisson structure for non-dissipative systems. We develop a canonical description for…

Classical Physics · Physics 2009-11-07 Sonnet Q H Nguyen , Lukasz A Turski