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Optimization-based parametric model order reduction via $\mathcal{H}_2\otimes\mathcal{L}_2$ first-order necessary conditions
arXiv - CS - Systems and Control Pub Date : 2021-03-04 , DOI: arxiv-2103.03136 Manuela Hund, Tim Mitchell, Petar Mlinarić, Jens Saak
arXiv - CS - Systems and Control Pub Date : 2021-03-04 , DOI: arxiv-2103.03136 Manuela Hund, Tim Mitchell, Petar Mlinarić, Jens Saak
In this paper, we generalize existing frameworks for
$\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad
class of parametric linear time-invariant systems. To this end, we derive
first-order necessary ptimality conditions for a class of structured
reduced-order models, and then building on those, propose a
stability-preserving optimization-based method for computing locally
$\mathcal{H}_2\otimes\mathcal{L}_2$-optimal reduced-order models. We also make
a theoretical comparison to existing approaches in the literature, and in
numerical experiments, show how our new method, with reasonable computational
effort, produces stable optimized reduced-order models with significantly lower
approximation errors.
中文翻译:
通过$ \ mathcal {H} _2 \ otimes \ mathcal {L} _2 $一阶必要条件进行基于优化的参数模型降阶
在本文中,我们将$ \ mathcal {H} _2 \ otimes \ mathcal {L} _2 $-最优模型阶约化的现有框架推广到一大类参数线性时不变系统。为此,我们为一类结构化降阶模型导出了一阶必要的最优性条件,然后在此基础上,提出了一种基于稳定性的优化优化方法来本地计算$ \ mathcal {H} _2 \ otimes \ mathcal {L} _2 $-最优降阶模型。我们还对文献中的现有方法进行了理论比较,并在数值实验中显示了我们的新方法如何以合理的计算量来生成稳定的,优化的降阶模型,且其近似误差显着降低。
更新日期:2021-03-05
中文翻译:
通过$ \ mathcal {H} _2 \ otimes \ mathcal {L} _2 $一阶必要条件进行基于优化的参数模型降阶
在本文中,我们将$ \ mathcal {H} _2 \ otimes \ mathcal {L} _2 $-最优模型阶约化的现有框架推广到一大类参数线性时不变系统。为此,我们为一类结构化降阶模型导出了一阶必要的最优性条件,然后在此基础上,提出了一种基于稳定性的优化优化方法来本地计算$ \ mathcal {H} _2 \ otimes \ mathcal {L} _2 $-最优降阶模型。我们还对文献中的现有方法进行了理论比较,并在数值实验中显示了我们的新方法如何以合理的计算量来生成稳定的,优化的降阶模型,且其近似误差显着降低。