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.
%0 Journal Article
%1 MorNU23
%A Morandin, Riccardo
%A Nicodemus, Jonas
%A Unger, Benjamin
%D 2023
%I Society for Industrial & Applied Mathematics (SIAM)
%J SIAM Journal on Scientific Computing
%K PN4 PN4-8 EXC2075
%N 4
%P A1690-A1710
%R 10.1137/22m149329x
%T Port-Hamiltonian Dynamic Mode Decomposition
%V 45
%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, 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.
@article{MorNU23,
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.},
added-at = {2023-09-26T20:58:38.000+0200},
author = {Morandin, Riccardo and Nicodemus, Jonas and Unger, Benjamin},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/287baad9cb05367445294d533c7411d26/simtech},
doi = {10.1137/22m149329x},
interhash = {e376402a167ee972f97e770d51124443},
intrahash = {87baad9cb05367445294d533c7411d26},
journal = {SIAM Journal on Scientific Computing},
keywords = {PN4 PN4-8 EXC2075},
month = jul,
number = 4,
pages = {A1690-A1710},
publisher = {Society for Industrial & Applied Mathematics (SIAM)},
timestamp = {2023-09-26T20:58:38.000+0200},
title = {Port-Hamiltonian Dynamic Mode Decomposition},
volume = 45,
year = 2023
}
