TY - JOUR
T1 - Fast Optimal $\mathcal{H}_2$ Model Reduction Algorithms Based on Grassmann Manifold Optimization
AU - Y. Xu & T. Zeng
JO - International Journal of Numerical Analysis and Modeling
VL - 4
SP - 972
EP - 991
PY - 2013
DA - 2013/10
SN - 10
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/ijnam/606.html
KW - $\mathcal{H}_2$ approximation, gradient flow, Grassmann manifold, model reduction, MIMO system, stability, large-scale sparse system.
AB - <p style="text-align: justify;">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.</p>