Finding the nearest bounded-real port-Hamiltonian system
Abstract
In this paper, we consider linear time-invariant continuous control systems which are bounded real, also known as scattering passive. Our main theoretical contribution is to show the equivalence between such systems and port-Hamiltonian (PH) systems whose factors satisfy certain linear matrix inequalities. Based on this result, we propose a formulation for the problem of finding the nearest bounded-real system to a given system, and design an algorithm combining alternating optimization and Nesterov's fast gradient method. This formulation also allows us to check whether a given system is bounded real by solving a semidefinite program, and provide a PH parametrization for it. We illustrate our proposed algorithms on real and synthetic data sets.
Cite
@article{arxiv.2501.11903,
title = {Finding the nearest bounded-real port-Hamiltonian system},
author = {Karim Cherifi and Nicolas Gillis and Punit Sharma},
journal= {arXiv preprint arXiv:2501.11903},
year = {2025}
}
Comments
20 pages, code, experiments and data available from https://gitlab.com/ngillis/nearestBRsysPHform