Numerical methods to compute a minimal realization of a port-Hamiltonian system

Abstract

Port-Hamiltonian (pH) systems are a very important modeling tool in almost all areas of systems and control, in particular in network based model of multi-physics multi-scale systems. They lead to remarkably robust models that can be easily interconnected. This paper discusses the derivation of pH models from time-domain input-output data. While a direct construction of pH models is still an open problem, we present three different indirect numerical methods for the realization of pH systems. The algorithms are implemented in MATLAB and their performance is illustrated via several numerical examples.

A non-intrusive method to inferring linear port-Hamiltonian realizations using time-domain data

“…The main contributions, so far, in the direction of inferring pH realizations from data can be found in [12], [13], [29]. The methods in [12], [13] are based on frequency-domain data.…”

“…Recently, in [12], a datadriven method to learning pH systems based on a solution of the passivity LMI [15] is proposed. Moreover, In [29], the authors proposed approaches to realize port-Hamiltonian systems using three different approaches. The goal is to learn a pH system in the form (1) for given input-output timedomain data.…”

“…In the following, we discuss a procedure that involve first inferring frequency response data [21], [29]. Then, we directly compute the underlying pH system using the method proposed in [13].…”

Solving matrix nearness problems via Hamiltonian systems, matrix factorization, and optimization

“…It is shown in [6] that every minimal passive system is equivalent to a PH system. It has also been recently shown to how robustly transform a passive and stable system into a robust PH system [90,23].…”

The difference between port-Hamiltonian, passive and positive real descriptor systems

“…If the system is behaviorally observable then ker A∩ker C = {0} and hence the existence of a pH formulation is equivalent to the existence of invertible solutions to the KYP inequality. Due to the interesting properties of pH systems, ideally, we want to obtain a pH representation for any passive system given in DAE form or given time domain data measurements [14]. In order to solve that problem we need to answer question (Q2).…”