Port-Hamiltonian Dynamic Mode Decomposition

Authors

Riccardo Morandin, Jonas Nicodemus, Benjamin Unger

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.

Citation

• Journal: SIAM Journal on Scientific Computing
• Year: 2023
• Volume: 45
• Issue: 4
• Pages: A1690–A1710
• Publisher: Society for Industrial & Applied Mathematics (SIAM)
• DOI: 10.1137/22m149329x

BibTeX

@article{Morandin_2023,
  title={{Port-Hamiltonian Dynamic Mode Decomposition}},
  volume={45},
  ISSN={1095-7197},
  DOI={10.1137/22m149329x},
  number={4},
  journal={SIAM Journal on Scientific Computing},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Morandin, Riccardo and Nicodemus, Jonas and Unger, Benjamin},
  year={2023},
  pages={A1690--A1710}
}

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References

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