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Koopman Reduced Order Control for Three Body Problem

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Document pages: 10 pages

Abstract: In this paper, we use a Circle Restricted Three-BodyProblem (CRTBP) to simulate the motion of a satellite. Then wereformulate this problem with the controller into the description using Koopmaneigenfunction. Although the original dynamical system is nonlinear, the Koopmaneigenfunction behaves linearly. Choosing Jacobi integral as theKoopman eigenfunction and using the zero velocity curve as the reference forcontrol, 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 fromthe earth to the moon or from the earth to the sun.

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