<p>Current indirect optimal control problem (IOCP) solvers, like beluga or PINs, use symbolic math to derive the necessary conditions to solve the IOCP. This limits the capability of IOCP solvers by only admitting symbolically representable functions. The purpose of this thesis is to present a framework that extends those solvers to derive the necessary conditions of an IOCP with fully numeric methods. With fully numeric methods, additional types of functions, including conditional logic functions and look-up tables can now be easily used in the IOCP solver.</p> <p><br></p> <p>This aim was achieved by implementing algorithmic differentiation (AD) as a method to derive the IOCP necessary conditions into a new solver called Giuseppe. The Brachistochrone problem was derived analytically and compared Giuseppe to validate the automatic derivation of necessary conditions. Two additional problems are compared and extended using this new solver. The first problem, the maximum cross-range problem, demonstrates a trajectory can be optimized indirectly while utilizing a conditional density function that switches as a function of height according to the 1976 U.S. atmosphere model. The second problem, the minimum time to climb problem, demonstrates a trajectory can be optimized indirectly while utilizing 6 interpolated look up tables for lift, drag, thrust, and atmospheric conditions. The AD method yields the exact same precision as the symbolic methods, rather than introducing numeric error as finite difference derivatives would with the benefit of admitting conditional switching functions and look-up tables. </p>

<p dir="ltr">The increased interest in deep space missions is creating an increased interest in cislunar space. The need for fast and efficient methods of traversing the lunar vicinity in creases as more spacecraft enter the region. This investigation discusses methods of low thrust transfer design in order to create low cost and low time of flight transfers. Indirect optimization is employed to compute minimum energy and minimum fuel transfers in the circular restricted three body problem. Sigmoid smoothing techniques are leveraged to ap proximate the optimal bang-coast-bang solution with continuous functions. The minimum fuel solution is employed as an initial guess to target an inertially fixed thrust direction transfer. This process is applied to a variety of cislunar orbital transfer problems. Transfers are constructed between orbits in the L1 halo, L2 halo, distant retrograde, and L4 short period orbit families. The resulting trajectories are compared to impulsive and free transfers from the literature based on the required propellant mass and time of flight.</p>