Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 972–991
Abstract
The optimal $\mathcal{H}_2$ model reduction is an important tool in studying dynamical systems of a large order and their numerical simulation. We formulate the reduction problem as a minimization problem over the Grassmann manifold. This allows us to develop a fast gradient flow algorithm suitable for large-scale optimal $\mathcal{H}_2$ model reduction problems. The proposed algorithm converges globally and the resulting reduced system preserves stability of the original system. Furthermore, based on the fast gradient flow algorithm, we propose a sequentially quadratic approximation algorithm which converges faster and guarantees the global convergence. Numerical examples are presented to demonstrate the approximation accuracy and the computational efficiency of the proposed algorithms.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-606
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 4 : pp. 972–991
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: $\mathcal{H}_2$ approximation gradient flow Grassmann manifold model reduction MIMO system stability large-scale sparse system.