Koopman-Based Lifting Techniques for Nonlinear Systems Identification
Koopman-Based Lifting Techniques for Nonlinear Systems Identification
复制标题
基于库普曼的非线性系统辨识提升技术
DOI：
10.1109/tac.2019.2941433
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发表时间：
2017
影响因子：
6.8
通讯作者：
Jorge M. Gonçalves
中科院分区：
文献类型：
--
作者：
A. Mauroy;Jorge M. Gonçalves
我们开发了一种新的提升技术的基础上的Koopman运营商的框架非线性系统识别。其关键思想是识别线性（无限维）Koopman算子在提升空间的可观测量，而不是识别的非线性系统的状态空间，一个过程中，在一个线性方法的非线性系统识别的结果。所提出的提升技术是一种间接的方法，不需要计算时间导数，因此非常适合于低采样率的数据集。考虑到不同的有限维子空间来逼近和识别Koopman算子，我们提出了两种数值格式：主方法和对偶方法。主要的方法是一个参数识别技术，可以准确地重建一个广泛的系统类的矢量场。对偶方法提供了在数据点处的向量场的估计，并且非常适合于识别具有小数据集的高维系统。本文介绍了这两种方法，提供了理论上的收敛性结果，并说明了提升技术与几个例子。
We develop a novel lifting technique for nonlinear system identification based on the framework of the Koopman operator. The key idea is to identify the linear (infinite dimensional) Koopman operator in the lifted space of observables, instead of identifying the nonlinear system in the state space, a process which results in a linear method for nonlinear systems identification. The proposed lifting technique is an indirect method that does not require to compute time derivatives and is therefore well-suited to low-sampling rate data sets. Considering different finite-dimensional subspaces to approximate and identify the Koopman operator, we propose two numerical schemes: a main method and a dual method. The main method is a parametric identification technique that can accurately reconstruct the vector field of a broad class of systems. The dual method provides estimates of the vector field at the data points and is well-suited to identify high-dimensional systems with small datasets. This paper describes the two methods, provides theoretical convergence results, and illustrates the lifting techniques with several examples.
从具有时变延迟的动力系统到圆图和库普曼算子
DOI：
10.1103/physreve.95.062214
发表时间：
--
期刊：
Physical review. E
影响因子：
--
作者：
D. Müller;A. Otto;G. Radons
通讯作者：
G. Radons