Koopman Reduced Order Control for Three Body Problem - Modern Mechanical Engineering

MME > Vol.9 No.1, February 2019

Koopman Reduced Order Control for Three Body Problem ()

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DOI: 10.4236/mme.2019.91003 1,079 Downloads 2,142 Views Citations

Author(s)

Haoze Tang

Affiliation(s)

John Carroll Catholic High School, Alabama, USA.

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.

KEYWORDS

Circle Restricted Three-Body Problem, Koopman Eigenfunction, Zero Velocity Curve

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.

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