Nonlinear model reduction based on stochastic obsevability
Nonlinear model reduction based on stochastic obsevability
复制标题
基于随机可观测性的非线性模型简化
DOI：
--
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
M. Yamakita
中科院分区：
文献类型：
--
作者：
Taijiro Kawamura;M. Yamakita
分析模型降阶方法的实用性是有限的。本文证明了基于本征正交分解（POD）的非线性模型降阶的最优性。POD是一种基于仿真的模型降阶方法，在非线性大系统中得到了广泛的应用，但一般没有理论背景。基于可观测性的解析非线性模型降阶还没有很好地提出。本文利用最优控制和最优估计之间的对偶关系导出了一种随机可观性，证明了当输入仅为随机信号时，基于可观性和基于模拟的加权方法是等价的。我们还展示了一个使用深度自动编码器的非线性模型降阶方法的例子。
The practical applicability of analytical model reduction methods is limited. In this paper, we show an optimality of Proper Orthogonal Decomposition (POD) based nonlinear model reduction. POD is a simulation-based model reduction method that has been widely applied to nonlinear large-scale systems, but there is no theoretical background in general. An observability-based analytical nonlinear model reduction is not well proposed. In this paper, after deriving a stochastic observability using a duality between optimal control and optimal estimation, we show that the observability-based and simulation-based methodologies with weights are equivalent when the input is only stochastic signal. We also show an example of nonlinear model reduction method using the deep autoencoder.
影响因子：
6.8
作者：
Astolfi, Alessandro
通讯作者：
Astolfi, Alessandro