A New Framework for $\mathcal{H}_2$-Optimal Model Reduction

Alessandro Castagnotto; Boris Lohmann

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arXiv · 1709.07270

A New Framework for $\mathcal{H}_2$-Optimal Model Reduction

Alessandro Castagnotto·Boris Lohmann

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Abstract

In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential interpolation and H2-optimal approxi- mations. The main advantage is given by a decoupling of the cost of optimization from the cost of reduction, resulting in a significant speedup in H2-optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing H2-optimal reduced models at a far lower cost than conventional algorithms. The paper ends with a brief discussion on how the idea behind the framework can be extended to approximate further system classes, thus showing that this truly is a general framework for interpolatory H2 reduction rather than just an additional reduction algorithm.

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Alessandro Castagnotto, Boris Lohmann. 2017-09-21. A New Framework for $\mathcal{H}_2$-Optimal Model Reduction. https://arxiv.org/abs/1709.07270

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