Application of Differential Transformation Based Algorithm to Find Optimal Interplanetary Low-Thrust Transfers

摘要

A new numerical method for solving nonlinear optimal control problems based on dif-ferential transformations is proposed for the first time to solve low-thrust interplanetary trajectory problems. The differential transformation algorithm is being used for solving the two-point boundary value problems that result from the indirect optimization approach. This algorithm converts the system of differential equations and its boundary conditions to a set of nonlinear algebraic equations, where solutions could be obtained more quickly. Moreover, the algorithm finds solutions in an analytical form. In this initial study, the algorithm is demonstrated on several interplanetary trajectories and compared with a multiple shooting method.