$H_2$ model reduction for diffusively coupled second-order networks by convex-optimization
Abstract
This paper provides an optimal scheme for reducing diffusively coupled second-order systems evolving over undirected networks. The aim is to find a reduced-order model that not only approximates the input-output mapping of the original system but also preserves crucial structures, such as the second-order form, asymptotically stability, and diffusive couplings. To this end, an optimal approach based on a convex relaxation is implemented to reduce the dimension, yielding a lower order asymptotically stable approximation of the original second-order network system. Then, a novel graph reconstruction approach is employed to convert the obtained model to a reduced system that is interpretable as an undirected diffusively coupled network. Finally, the effectiveness of the proposed method is illustrated via a large-scale networked mass-spring-damper system.
Cite
@article{arxiv.2104.04321,
title = {$H_2$ model reduction for diffusively coupled second-order networks by convex-optimization},
author = {Lanlin Yu and Xiaodong Cheng and Jacquelien M. A. Scherpen and Junlin Xiong},
journal= {arXiv preprint arXiv:2104.04321},
year = {2021}
}