Model Order Reduction for Differential-Algebraic Equations: A Survey
Model Order Reduction for Differential-Algebraic Equations: A Survey
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DOI：
10.1007/978-3-319-46618-7_3
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
P. Benner;T. Stykel
中科院分区：
文献类型：
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作者：
P. Benner;T. Stykel
在本文中，我们讨论描述符系统（即用微分代数方程描述动力学的系统）的模型降阶问题。我们关注线性描述符系统，因为存在多种方法，而非线性描述符系统的模型降阶迄今为止尚未受到足够的关注。在撰写本文时，线性状态空间系统的模型降阶已经成为一个研究主题大约 50 年，现在可以被认为是一个成熟的领域。线性描述符系统的扩展通常需要额外处理系统代数部分所施加的约束。对于几乎所有方法来说，这都会导致一些技术困难，而这些问题直到最近十年才得到彻底解决。我们将重点关注这些发展，特别是与平衡截断和有理插值相关的流行方法。我们将回顾将这些方法扩展到描述符系统的努力，并将所谓的随机平衡截断方法扩展到描述符系统，这是迄今为止在文献中找不到的。
In this paper, we discuss the model order reduction problem for descriptor systems, that is, systems with dynamics described by differential-algebraic equations. We focus on linear descriptor systems as a broad variety of methods for these exist, while model order reduction for nonlinear descriptor systems has not received sufficient attention up to now. Model order reduction for linear state-space systems has been a topic of research for about 50 years at the time of writing, and by now can be considered as a mature field. The extension to linear descriptor systems usually requires extra treatment of the constraints imposed by the algebraic part of the system. For almost all methods, this causes some technical difficulties, and these have only been thoroughly addressed in the last decade. We will focus on these developments in particular for the popular methods related to balanced truncation and rational interpolation. We will review efforts in extending these approaches to descriptor systems, and also add the extension of the so-calledstochastic balanced truncationmethod to descriptor systems which so far cannot be found in the literature.