Related papers: A novel energy-based modeling framework
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…
This paper develops a comprehensive mathematical framework for energy-based modeling of physical systems, with particular emphasis on preserving fundamental structural properties throughout the modeling and discretization process. The…
This paper presents a generalized energy-based modeling framework extending recent formulations tailored for differential-algebraic equations. The proposed structure, inspired by the port-Hamiltonian formalism, ensures passivity, preserves…
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…
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…
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…
This paper addresses the regulation and trajectory-tracking problems for two classes of weakly coupled electromechanical systems. To this end, we formulate an energy-based model for these systems within the port-Hamiltonian framework. Then,…
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…
A general framework for the numerical approximation of evolution problems is presented that allows to preserve exactly an underlying Hamiltonian- or gradient structure. The approach relies on rewriting the evolution problem in a particular…
Port-Hamiltonian systems provide an energy-based formulation with a model class that is closed under structure preserving interconnection. For continuous-time systems these interconnections are constructed by geometric objects called Dirac…
We provide a fully nonlinear port-Hamiltonian formulation for discrete elastodynamical systems as well as a structure-preserving time discretization. The governing equations are obtained in a variational manner and represent index-1…
In this paper we present a complete framework for the energy-stable simulation of stratified incompressible flow in channels, using the one-dimensional two-fluid model. Building on earlier energy-conserving work on the basic two-fluid…
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…
In this article, we consider a one-dimensional Timoshenko system subject to different types of dissipation (linear and nonlinear dampings). Based on a combination between the finite element and the finite difference methods, we design a…
We study the systematic numerical approximation of a class of Allen-Cahn type problems modeling the motion of phase interfaces. The common feature of these models is an underlying gradient flow structure which gives rise to a decay of an…
Hydrogen's growing role in the transition towards climate-neutral energy systems necessitates structured modeling frameworks. Existing gas network models, largely developed for natural gas, fail to capture hydrogen systems distinct…
We employ a port-Hamiltonian approach to model nonlinear rigid multibody systems subject to both position and velocity constraints. Our formulation accommodates Cartesian and redundant coordinates, respectively, and captures kinematic as…
An energy-based discontinuous Galerkin method for the advective wave equation is proposed and analyzed. Energy-conserving or energy-dissipating methods follow from simple, mesh-independent choices of the inter-element fluxes, and both…
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…
We consider the discretization and subsequent model reduction of a system of partial differential-algebraic equations describing the propagation of pressure waves in a pipeline network. Important properties like conservation of mass,…