Infinite-Dimensional Port-Hamiltonian Systems with a Moving Interface

This thesis deals with the formulation and analysis of two systems of conservation laws defined on two complementary intervals and coupled by some moving interface as a single infinite-dimensional port-Hamiltonian system. This approach may be regarded as an extension of the well-established mathemat...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Author Kilian, Alexander
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 18.01.2023
Subjects
Conservation laws
Hamiltonian functions
Power flow
Transmission lines
Well posed problems
Online AccessGet full text

Cover

More Information
Summary:This thesis deals with the formulation and analysis of two systems of conservation laws defined on two complementary intervals and coupled by some moving interface as a single infinite-dimensional port-Hamiltonian system. This approach may be regarded as an extension of the well-established mathematical framework of boundary port-Hamiltonian systems, i.e., infinite-dimensional Hamiltonian systems interacting with its physical environment. In order to keep track of the power flow at the position of the interface, we introduce interface port variables. We provide a well-posed port-Hamiltonian model of two distinct systems of conservation laws defined on two complementary, 1-dimensional spatial domains that are coupled by a fixed interface, and illustrate this result by reference to two transmission lines coupled through a resistor. Furthermore, we discuss under which boundary and interface conditions this system is exponentially stable. Since the formulation in case of a moving interface is quite troubled, we present some results that may be regarded as a first step towards a well-posed model, and debate the main issues that have to be tackled in the future.
ISSN:2331-8422