Stochastic port--Hamiltonian systems

TL;DR

This paper extends port-Hamiltonian systems to include stochastic elements, allowing for interconnected systems with intrinsic noise, and demonstrates that power-preserving interconnections maintain the stochastic port-Hamiltonian structure.

Contribution

It introduces a formal framework for stochastic port-Hamiltonian systems, incorporating intrinsic noise in ports and showing closure under power-preserving interconnections.

Findings

The framework models systems with intrinsic stochastic ports.

Interconnections preserve the stochastic port-Hamiltonian structure.

Extends deterministic port-Hamiltonian theory to stochastic settings.

Abstract

In the present work we formally extend the theory of port-Hamiltonian systems to include random perturbations. In particular, suitably choosing the space of flow and effort variables we will show how several elements coming from possibly different physical domains can be interconnected in order to describe a dynamic system perturbed by general continuous semimartingale. Relevant enough, the noise does not enter into the system solely as an external random perturbation, since each port is itself intrinsically stochastic. Coherently to the classical deterministic setting, we will show how such an approach extends existing literature of stochastic Hamiltonian systems on pseudo-Poisson and pre-symplectic manifolds. Moreover, we will prove that a power-preserving interconnection of stochastic port-Hamiltonian systems is a stochastic port-Hamiltonian system as well.