Deep Learning Based Dynamics Identification and Linearization of Orbital
  Problems using Koopman Theory
George Nehma Madhur Tiwari Manasvi Lingam
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.