Optimal Control of Interplanetary Trajectories Using Electrical Propulsion with Discrete Thrust Levels

This work proposes a solution to the optimal closed-loop trajectory control of interplanetary missions, with solar-electric propulsion system that provides discrete thrust levels. The solution is either suitable to the case of discrete multi-level electrical engine, or a cluster of several unidirectional engines. The objective is to guide the spacecraft from an initial state to a final state (position and velocity) at an exact given time, with minimum fuel expenditure. The optimization is based on the approach of "neighboring optimal trajectory": given a nominal trajectory (close to, but not necessarily the optimal one), the objective is to control the spacecraft along an optimal neighboring trajectory. In this approach, when a deviation from the planned trajectory is developed, a new neighboring optimal trajectory is calculated to obtain the required end-condition, while beginning at the current point. Using this approach, we assure lower fuel consumption, comparing to another control policy that tries to maintain uncompromisingly a nominal optimal trajectory. The paper presents the development of the control law for this problem. An efficient algorithm for the numerical solution of the optimal controller is proposed and demonstrated for two examples: correction of satellite orbit around the moon, and an interplanetary rendezvous mission to Mercury.