FAST OPTIMAL H2 MODEL REDUCTION ALGORITHMS BASED ON GRASSMANN MANIFOLD OPTIMIZATION

The optimal H2 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 H2 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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