Port-Hamiltonian systems with energy and power ports

TL;DR

This paper extends the port-Hamiltonian framework by introducing energy ports, allowing the modeling of constrained Hamiltonian systems with input-dependent Hamiltonians, thus broadening the framework's applicability.

Contribution

The paper introduces a novel extension of the port-Hamiltonian framework by incorporating energy ports through augmentation of the Lagrangian submanifold with external variables.

Findings

The extended framework can model constrained Hamiltonian systems with input-dependent Hamiltonians.

The new energy port concept generalizes existing port-Hamiltonian structures.

The approach maintains the geometric structure of the original framework.

Abstract

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 energy port. We show that in the most general case, the extension describes constrained Hamiltonian systems whose Hamiltonian function depends on inputs.