Orbital Station-Keeping in the Earth-Moon System via Nonlinear Backstepping

A nonlinear orbital station-keeping solution for the circular and elliptic versions of the Earth-Moon Restricted Three-Body Problem (R3BP) is developed via a backstepping technique. Formal guarantees for global asymptotic stability (GAS) are attained, as shown through Lyapunov's stability theory. The adequacy of the proposed control law is evaluated through the means of numerical trials over closed periodic solutions of the circular and elliptic R3BPs. The ramifications of the control gain choice are carefully studied and simulated.