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 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.
%0 Journal Article
%1 MorNU22
%A Morandin, Riccardo
%A Nicodemus, Jonas
%A Unger, Benjamin
%D 2022
%J ArXiv e-print 2204.13474
%K myown
%R 10.48550/arXiv.2204.13474
%T Port-Hamiltonian Dynamic Mode Decomposition
%X 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 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.
@article{MorNU22,
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 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.},
added-at = {2022-08-26T15:14:29.000+0200},
author = {Morandin, Riccardo and Nicodemus, Jonas and Unger, Benjamin},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/292eb8f542726d58033e6bab083ae3eee/jonasnicodemus},
doi = {10.48550/arXiv.2204.13474},
interhash = {05225c34b34e73595cb2b67a061438a5},
intrahash = {92eb8f542726d58033e6bab083ae3eee},
journal = {ArXiv e-print 2204.13474},
keywords = {myown},
pubdate = {2022-04-28},
timestamp = {2022-08-26T13:14:29.000+0200},
title = {Port-Hamiltonian Dynamic Mode Decomposition},
year = 2022
}
