On the port-Hamiltonian representation of systems described by partial differential equations

TL;DR

This paper develops a novel port-Hamiltonian framework for infinite-dimensional systems described by partial differential equations, emphasizing different structural scenarios and diverging from traditional energy-variable-based representations.

Contribution

It introduces a new port-Hamiltonian representation for PDE systems that does not rely solely on energy variables, covering both differential and non-differential operator cases.

Findings

New port-Hamiltonian representation for PDEs

Applicable to both differential and non-differential cases

Provides alternative to Stokes-Dirac structure based models

Abstract

We consider infinite dimensional port-Hamiltonian systems. Based on a power balance relation we introduce the port-Hamiltonian system representation where we pay attention to two different scenarios, namely the non-differential operator case and the differential operator case regarding the structural mapping, the dissipation mapping and the in/output mapping. In contrast to the well-known representation on the basis of the underlying Stokes-Dirac structure our approach is not necessarily based on using energy-variables which leads to a different port-Hamiltonian representation of the analyzed partial differential equations.