Robust control strategy of periodic orbits via a hybrid multiple-shooting approach

This manuscript proposes a systematic approach for the design of a nominal robust trajectory and an associated closed-loop control law, where quantitative information concerning uncertainty on the system dynamics and stochastic navigation errors are directly accounted for in the optimization process. More precisely, a linear feedback control law is sought in order to steer the probability distribution of the spacecraft state towards a target distribution at an assigned final time. A hybrid multiple-shooting approach is used, where the mean trajectory and the open-loop controls are optimized according to a multiple-shooting scheme, while a single-shooting scheme is adopted for propagating higher-order statistical moments of the spacecraft state distribution, which varies according to the closed-loop feedback gains to be optimized. The proposed method is applied to perform orbital control of a spacecraft placed on a periodic orbit in the CR3BP. Recurring corrective maneuvers are evaluated and imparted on the probe to keep the deviation from the nominal trajectory within a prescribed limit.