论文标题
学习有限的库普曼可观察到：稳定性，连续性和可控性的结果
Learning Bounded Koopman Observables: Results on Stability, Continuity, and Controllability
论文作者
论文摘要
Koopman操作员是用于研究动力系统的有用分析工具 - 受控和不受控制。例如，Koopman本征可以提供有关基础动力学系统的非本地稳定性信息。非线性系统的Koopman表示通常是使用机器学习方法来计算的，该方法试图将Koopman本征函数表示为非线性状态测量的线性组合。因此，重要的是要了解这些本征函数是否可以通过机器学习成功获得，以及以这种方式计算的征征可以告诉我们有关基础系统的信息。为此，本文介绍了与最小假设相关的连续性，稳定性和控制局限性的分析，并提供了将这些属性与机器学习计算Koopman表示的能力相关的讨论。
The Koopman operator is an useful analytical tool for studying dynamical systems -- both controlled and uncontrolled. For example, Koopman eigenfunctions can provide non-local stability information about the underlying dynamical system. Koopman representations of nonlinear systems are commonly calculated using machine learning methods, which seek to represent the Koopman eigenfunctions as a linear combinations of nonlinear state measurements. As such, it is important to understand whether, in principle, these eigenfunctions can be successfully obtained using machine learning and what eigenfunctions calculated in this way can tell us about the underlying system. To that end, this paper presents an analysis of continuity, stability and control limitations associated with Koopman eigenfunctions under minimal assumptions and provides a discussion that relates these properties to the ability to calculate Koopman representations with machine learning.
