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Brunton, S.L., Brunton, B.W., Proctor, J.L. and Kutz, J.N. (2016) Koopman Invariant Subspaces and Finite Linear Representations of Nonlinear Dynamical Systems for Control. PLoS ONE, 11, e0150171.
https://doi.org/10.1371/journal.pone.0150171

has been cited by the following article:

• TITLE: Data-Driven Nonlinear Control for Orbit Transfer: From the Earth to Moon and L4/5

  AUTHORS: Xianyang Chen

  KEYWORDS: Restricted Three Body Problem, Koopman Eigenfunction, Non-Linear System

  JOURNAL NAME: Modern Mechanical Engineering, Vol.9 No.1, January 17, 2019

  ABSTRACT: From the recent thirty years, scientists will never stop exploring the outer space. To assist the development of travelling into the universe, I devote myself into providing theoretical support and future indications for designing the optimal orbit for satellite to travel in a Three-Body System. This paper offers the optimal orbit for satellite to change path in the earth-moon system. Also, it provides the path for the satellite to use the least fuel to go to the L4 and L5 Lagrange points. These inspiring results are obtained through several steps: to solve the problems caused by the non-linear character of Three-Body System, I use Koopman eigenfunction to change the system into a linear one. Data-driven method is adopted to find the most suitable Koopman eigenfunction to apply control. The traditional LQR operator for linear system is used to design the optimal orbit for the satellite.