A Structural Observation on port-Hamiltonian Systems

TL;DR

This paper characterizes boundary conditions for port-Hamiltonian systems on intervals that ensure the operators generate contractive semigroups, using structural transformations and providing well-posedness results for related control problems.

Contribution

It offers a novel structural approach to analyze port-Hamiltonian operators and characterizes all boundary conditions leading to m-accretive realizations, extending well-posedness results.

Findings

Characterization of boundary conditions for m-accretive port-Hamiltonian operators

Transformation of operators to simpler derivative forms on reference intervals

Well-posedness results for associated control problems

Abstract

We study port-Hamiltonian systems on a familiy of intervals and characterise all boundary conditions leading to $m$-accretive realisations of the port-Hamiltonian operator and thus to generators of contractive semigroups. The proofs are based on a structural observation that the port-Hamiltonian operator can be transformed to the derivative on a familiy of reference intervals by suitable congruence relations allowing for studying the simpler case of a transport equation. Moreover, we provide well-posedness results for associated control problems without assuming any additional regularity of the operators involved.