An iterative model order reduction method for large-scale dynamical systems

Authors

  • Kouki Mohamed Universit´e de Tunis El Manar, ´ Ecole Nationale d’Ingenieurs de Tunis, Laboratoire de Recherche Analyse et Commande des Syst`emes.
  • Abbes Mehdi Universit´e de Carthage, ´ Ecole Nationale d’Ing´enieurs de Carthage, Laboratoire de Recherche Analyse et Commande des Syst`eme
  • Mami Abdelkader Universit´e de Tunis El Manar, Facult´e des Sciences de Tunis, Laboratoire de Recherche Analyse et Commande des Syst`emes

DOI:

https://doi.org/10.21914/anziamj.v59i0.9622

Keywords:

AORA, SVD, Gramian, large scale, Krylov, moment matching, H.

Abstract

We present a new iterative model order reduction method for large-scale linear time-invariant dynamical systems, based on a combined singular value decomposition–adaptive-order rational Arnoldi (SVD-AORA) approach. This method is an extension of the SVD-rational Krylov method. It is based on two-sided projections: the SVD side depends on the observability Gramian by the resolution of the Lyapunov equation, and the Krylov side is generated by the adaptive-order rational Arnoldi based on moment matching. The use of the SVD provides stability for the reduced system, and the use of the AORA method provides numerical efficiency and a relative lower computation complexity. The reduced model obtained is asymptotically stable and minimizes the error (H2 and H) between the original and the reduced system. Two examples are given to study the performance of the proposed approach. doi:10.1017/S1446181117000049

Published

2017-09-05

Issue

Section

Articles for Printed Issues