Finding the nearest bounded-real port-Hamiltonian system

TL;DR

This paper establishes a theoretical link between bounded-real control systems and port-Hamiltonian systems, and introduces algorithms to find the nearest such system to a given one, with practical applications demonstrated on data.

Contribution

It provides a new characterization of bounded-real systems as port-Hamiltonian systems and develops algorithms for their approximation and verification.

Findings

Algorithm successfully finds nearest bounded-real systems.

Semidefinite programming can verify bounded-real property.

Applications on real and synthetic data validate the approach.

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.