H2 model reduction for diffusively coupled second-order networks by convex-optimization

Lanlin Yu, Xiaodong Cheng, Jacquelien M.A. Scherpen*, Junlin Xiong

*Corresponding author for this work

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Abstract

This paper provides an H2 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 H2 optimal approach based on a convex relaxation is used 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.

Original languageEnglish
Article number110118
Number of pages9
JournalAutomatica
Volume137
DOIs
Publication statusPublished - Mar-2022

Keywords

  • Convex-optimization
  • Diffusive coupling
  • H model reduction
  • Linear matrix inequality
  • Second-order networks

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