Port-Hamiltonian Dynamic Mode Decomposition

TL;DR

This paper introduces a physics-informed system identification approach for passive linear systems using port-Hamiltonian frameworks, modifying dynamic mode decomposition for continuous-time systems, and demonstrating efficiency through numerical examples.

Contribution

It develops a novel port-Hamiltonian system identification method that guarantees energy dissipation and adapts dynamic mode decomposition for continuous-time systems.

Findings

Effective numerical method for port-Hamiltonian system realization.

Guaranteed dissipation inequality in identified models.

Validated approach with multiple numerical examples.

Abstract

We present a novel physics-informed system identification method to construct a passive linear time-invariant system. In more detail, for a given quadratic energy functional, measurements of the input, state, and output of a system in the time domain, we find a realization that approximates the data well while guaranteeing that the energy functional satisfies a dissipation inequality. To this end, we use the framework of port-Hamiltonian (pH) systems and modify the dynamic mode decomposition, respectively operator inference, to be feasible for continuous-time pH systems. We propose an iterative numerical method to solve the corresponding least-squares minimization problem. We construct an effective initialization of the algorithm by studying the least-squares problem in a weighted norm, for which we present the analytical minimum-norm solution. The efficiency of the proposed method is demonstrated with several numerical examples.