The study of the Two-Body and Circular Restricted Three-Body Problems in the
field of aerospace engineering and sciences is deeply important because they
help describe the motion of both celestial and artificial satellites. With the
growing demand for satellites and satellite formation flying, fast and
efficient control of these systems is becoming ever more important. Global
linearization of these systems allows engineers to employ methods of control in
order to achieve these desired results. We propose a data-driven framework for
simultaneous system identification and global linearization of both the
Two-Body Problem and Circular Restricted Three-Body Problem via deep
learning-based Koopman Theory, i.e., a framework that can identify the
underlying dynamics and globally linearize it into a linear time-invariant
(LTI) system. The linear Koopman operator is discovered through purely
data-driven training of a Deep Neural Network with a custom architecture. This
paper displays the ability of the Koopman operator to generalize to various
other Two-Body systems without the need for retraining. We also demonstrate the
capability of the same architecture to be utilized to accurately learn a
Koopman operator that approximates the Circular Restricted Three-Body Problem.

通过深度学习的 Koopman 理论，我们提出了一个数据驱动的框架，用于同时对二体问题和圆形受限三体问题进行系统识别和全局线性化，并将其线性化为线性时不变系统。该论文展示了 Koopman 算子具有泛化到各种其他二体系统的能力，而无需重新训练。我们还证明了同样的架构可以用于准确学习近似圆形受限三体问题的 Koopman 算子。