A behavioural approach to port-controlled systems

TL;DR

This paper uses category theory to analyze port-controlled Hamiltonian systems, viewing them as extensions of closed Hamiltonian systems with specific port structures, applicable to various physical models.

Contribution

It introduces a categorical framework to understand port-control structures as system extensions, broadening the analysis of Hamiltonian and metriplectic systems.

Findings

Categorical description of port-Hamiltonian systems as system extensions

Identification of port structures with desired properties

Application to Hamiltonian and metriplectic systems

Abstract

We give insight in the structure of port-Hamiltonian systems as control systems in between two closed Hamiltonian systems. Using the language of category theory, we identify systems with their behavioural representation and view a port-control structure with desired structural properties on a given closed system as an extension of this system which itself may be embedded in a "larger" closed system. The latter system describes the nature of the ports (e.g. Hamiltonian, metriplectic etc.). This point of view allows us to describe meaningful port-control structures for a large family of systems, which is illustrated with Hamiltonian and metriplectic systems.