Low-Thrust Optimization for Lengthy Cislunar Transfers Using Nested B-Spline Control

While mathematically well-posed, many optimal control problem formulations become increasingly numerically ill-conditioned as their size increases. A novel multiple shooting with adjoint sensitivities framework solves an unusually long orbit raising from a geosynchronous transfer orbit to a near-rectilinear halo orbit. Nested B-splines are proposed for low-thrust control parameterization that is further compressed through singular value decomposition. In addition, a new time-regularizing independent variable for the [Formula: see text] orbital elements is introduced to eliminate numerical challenges encountered for cislunar transfers. The main low-thrust scenario considers the launcher performance at the starting orbit and, moreover, a maximum duration of eclipse inequality constraint. This discrete path constraint is treated by forming adjoint equations for a system of ordinary differential equations with an implicitly defined endpoint. A numerical experiment on integration schemes and two minimum-propellant scenarios are also provided. Lastly, a proof that the solution of a shooting formulation satisfies the first-order necessary conditions of optimality is developed for a Bolza problem using functional derivatives.