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Koopman Reduced Order Control for Three Body Problem
John Carroll Catholic High School, Alabama, USA
- 1 John Carroll Catholic High School, Alabama, USA
Modern Mechanical Engineering·Volume 09 (2019)·Pages 20–29·Published 16 January 2019·DOI10.4236/mme.2019.91003
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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.
KeywordsCircle Restricted Three-Body ProblemKoopman EigenfunctionZero Velocity Curve
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