Koopman Reduced Order Control for Three Body Problem ()
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.
Share and Cite:
Tang, H. (2019) Koopman Reduced Order Control for Three Body Problem.
Modern Mechanical Engineering,
9, 20-29. doi:
10.4236/mme.2019.91003.