Analytical mathematical feedback guidance scheme for low-thrust orbital plane change maneuvers

Abstract

This paper which is based on neighboring optimal control investigates the application of an analytical feedback guidance scheme for the problems of low-thrust orbital transfer. Neighboring optimal control is one of the methods that has been proposed for the closed-loop optimal guidance. This method focuses on expanding the cost function to second order and examining the robustness of the system by the feedback law gains. At first, the open-loop analytical guidance policy is considered as the optimal thrust steering program that will transfer the vehicle from the inclined low earth orbits to the high earth orbits. Secondly, proper feedback optimal guidance laws are analytically obtained to maintain the trajectories around their optimum with assessed disturbances. The proposed guidance scheme is distinguished for two desired performance indices as minimum-time and minimum-effort. Finally performance indices are compared and the best policy is obtained regarding the robustness of the two performance indices against disturbances.