Related papers: Differential algebraic system nodes
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…
Operator splitting methods allow to split the operator describing a complex dynamical system into a sequence of simpler subsystems and treat each part independently. In the modeling of dynamical problems, systems of (possibly coupled)…
We consider a class of differential-algebraic equations (DAEs) with index zero in an infinite dimensional Hilbert space. We define a space of consistent initial values, which lead to classical continuously differential solutions for the…
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…
Many models of physical systems, such as mechanical and electrical networks, exhibit algebraic constraints that arise from subsystem interconnections and underlying physical laws. Such systems are commonly formulated as…
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…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
In this paper we study the representation of partial differential equations (PDEs) as abstract differential-algebraic equations (DAEs) with dissipative Hamiltonian structure (adHDAEs). We show that these systems not only arise when there…
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…
High index differential algebraic equations (DAEs) are ordinary differential equations (ODEs) with constraints and arise frequently from many mathematical models of physical phenomenons and engineering fields. In this paper, we generalize…
For nonlinear differential-algebraic equations (DAEs), we define two kinds of equivalences, namely, the external and internal equivalence. Roughly speaking, the word "external" means that we consider a DAE (locally) everywhere and…
The solvability for infinite dimensional differential algebraic equations possessing a resolvent index and a Weierstra{\ss} form is studied. In particular, the concept of integrated semigroups is used to determine a subset on which…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
Carleman linearization is a mathematical technique that transforms nonlinear dynamical systems into infinite-dimensional linear systems, enabling simplified analysis. Initially developed for ordinary differential equations (ODEs) and later…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
Power system dynamics are generally modeled by high dimensional nonlinear differential-algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing…
A previous article was devoted to an analysis of the symmetry properties of a class of first-order delay ordinary differential systems (DODSs). Here we concentrate on linear DODSs. They have infinite-dimensional Lie point symmetry groups…
We develop compositional learning algorithms for coupled dynamical systems, with a particular focus on electrical networks. While deep learning has proven effective at modeling complex relationships from data, compositional couplings…
Differential algebraic equations (DAEs) describe the temporal evolution of systems that obey both differential and algebraic constraints. Of particular interest are systems that contain implicit relationships between their components, such…
The nature of so-called differential-algebraic operators and their approximations is constitutive for the direct treatment of higher-index differential-algebraic equations. We treat first-order differential-algebraic operators in detail and…