Nonlinear optimal control of the continuous low-thrust transfer between Halo orbits

A nonlinear optimal control strategy is formulated to design optimal continuous low-thrust transfers between three dimensional Halo orbits in the vicinity of the second libration point of the Sun-Earth system. The nonlinear optimal control method based on the circular restricted three-body problem model, which uses the dual variable principle, is transformed into nonlinear algebraic equations for transfer missions between Halo orbits. The nonlinear optimal control is investigated by numerical simulations and compared with linear optimal control strategy. It is shown that the necessity of the proposed method and the thrust required can be provided by next generation electric propulsion system.