Relaxed Convex Approximation for Optimal Control in Cislunar Space

This thesis develops a method of optimal control for a spacecraft in the region between the Earth and the Moon known as cislunar space. The optimal control method is developed through a modern optimization technique called “convex relaxation” to achieve a formulation that can be reliably solved by numerical computation tools. The primary research objective is to evaluate the efficacy of this method in accommodating the physical thrust constraints of a spacecraft. This approach is tested in simulation with an unstable halo orbit around the Moon in the circular restricted three-body problem (CR3BP) model. The simulation incorporates realistic disruptions from insertion, navigation, and burn errors. Analysis is performed over multiple simulation runs and focuses on control performance metrics, including total control effort (delta-V) and final trajectory state deviations in position and velocity. The results demonstrate that the convex relaxation formulation reliably achieves optimal control in a computationally efficient manner.