A Method for Solving the Multi-Extreme Problem of Optimizing Trajectories of a Spacecraft with an Elecrto-Jet Propulsion System’s Thrust

— The study proposes a regular method that allows one to find (one or more) solutions of a multi-extreme problem for optimizing the transfer of a spacecraft, equipped with a perfectly controlled electro-jet propulsion system, in a central gravitational field. The method consists of three main stages. In the first stage, using an algorithm based on the Bellman optimality principle, for various values of angular range, the composite transporting trajectories are generated in an impulse formulation. In the second stage, in the vicinity of these trajectories, the first-approximation trajectories with continuous control are formed using the local variation method. At the third stage, the latter trajectories are used to find an accurate solution of a nonlinear boundary value problem. Then, the results are analyzed to determine the optimum. The numerical example of using this method to construct optimal trajectories of spacecraft transfer from Earth to the Apophis asteroid is presented.