Optimal control for orbital transfer of LEO satellites with low-thrust engines

In this work, we present an application of the optimal control theory to orbital transfer of Low Earth Orbit satellites. The optimal control problem is treated with Dynamic Programming techniques which require solving the Hamilton–Jacobi–Bellman equations on a suitable state space, with the reconstruction of the optimal controls in a static feedback form. This study sets the problem first in planar form, thus working in a four-dimensional state space, and then in the three-dimensional case (thus working in a six-dimensional state space). We will focus on the implementation of various techniques to speed up the computation, and asses the accuracy of the numerical solution. This project born from the attempt of evaluating and applying direct methods of optimal control techniques based on Dynamic Programming, as a complementary approach to the well known indirect methods, as Pontryagin. The final aim is to treat the case of low thrust engines from real use cases in the 3D full problem, as we will show in this work.