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