Port-Hamiltonian Dynamic Mode Decomposition
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.
Cite
@article{arxiv.2204.13474,
title = {Port-Hamiltonian Dynamic Mode Decomposition},
author = {Riccardo Morandin and Jonas Nicodemus and Benjamin Unger},
journal= {arXiv preprint arXiv:2204.13474},
year = {2023}
}