%0 Journal Article
%T Koopman Reduced Order Control for Three Body Problem
%A Haoze Tang
%J Modern Mechanical Engineering
%P 20-29
%@ 2164-0181
%D 2019
%I Scientific Research Publishing
%R 10.4236/mme.2019.91003
%X In this paper, we use a Circle Restricted Three</span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">-</span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">Body
Problem (CRTBP) to simulate the motion of a satellite.</span></span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">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</span></span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">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</span></span></span><span><span><span style=\"font-family:&quot;\"> </span></span></span><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\"><span style=\"font-family:Verdana;\">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.
%K Circle Restricted Three-Body Problem
%K Koopman Eigenfunction
%K Zero  Velocity Curve
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=90354