Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems

Authors

S. Chaturantabut, C. Beattie, S. Gugercin

Abstract

This paper presents a structure-preserving model reduction approach applicable to large-scale, nonlinear port-Hamiltonian systems. Structure preservation in the reduction step ensures the retention of port-Hamiltonian structure which, in turn, assures the stability and passivity of the reduced model. Our analysis provides a priori error bounds for both state variables and outputs. Three techniques are considered for constructing bases needed for the reduction: one that utilizes proper orthogonal decompositions; one that utilizes $ \mathcal{H}2/\mathcal{H}{\infty} $-derived optimized bases; and one that is a mixture of the two. The complexity of evaluating the reduced nonlinear term is managed efficiently using a modification of the discrete empirical interpolation method (DEIM) that also preserves port-Hamiltonian structure. The efficiency and accuracy of this model reduction framework are illustrated with two examples: a nonlinear ladder network and a tethered Toda lattice.

Citation

Journal: SIAM Journal on Scientific Computing
Year: 2016
Volume: 38
Issue: 5
Pages: B837–B865
Publisher: Society for Industrial & Applied Mathematics (SIAM)
DOI: 10.1137/15m1055085

BibTeX

@article{Chaturantabut_2016,
  title={{Structure-Preserving Model Reduction for Nonlinear Port-Hamiltonian Systems}},
  volume={38},
  ISSN={1095-7197},
  DOI={10.1137/15m1055085},
  number={5},
  journal={SIAM Journal on Scientific Computing},
  publisher={Society for Industrial & Applied Mathematics (SIAM)},
  author={Chaturantabut, S. and Beattie, C. and Gugercin, S.},
  year={2016},
  pages={B837--B865}
}

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