Structure-preserving Model Reduction for Nonlinear Port-Hamiltonian Systems
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 -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.
Cite
@article{arxiv.1601.00527,
title = {Structure-preserving Model Reduction for Nonlinear Port-Hamiltonian Systems},
author = {Saifon Chaturantabut and Chris Beattie and Serkan Gugercin},
journal= {arXiv preprint arXiv:1601.00527},
year = {2016}
}