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https://doi.org/10.2514/2.4862

has been cited by the following article:

• TITLE: Koopman Reduced Order Control for Three Body Problem

  AUTHORS: Haoze Tang

  KEYWORDS: Circle Restricted Three-Body Problem, Koopman Eigenfunction, Zero Velocity Curve

  JOURNAL NAME: Modern Mechanical Engineering, Vol.9 No.1, February 1, 2019

  ABSTRACT: In this paper, we use a Circle Restricted Three-Body Problem (CRTBP) to simulate the motion of a satellite. Then we reformulate this problem with the controller into the description using Koopman eigenfunction. Although the original dynamical system is nonlinear, the Koopman eigenfunction behaves linearly. Choosing Jacobi integral as the Koopman eigenfunction and using the zero velocity curve as the reference for control, we are allowed to combine well-developed Linear Quadratic Regulator (LQR) controller to design a nonlinear controller. Using this approach, we design the low thrust orbit transfer strategy for the satellite flying from the earth to the moon or from the earth to the sun.