Optimal guidance of aeroassisted transfer vehicles based on matched asymptotic expansions

In this paper we address and clarify a number of issues related to matched asymptotic expansion analysis of skip trajectories or any class of problems that give rise to inner layers that are not associated directly with satisfying boundary conditions. The procedure for matching inner and outer solutions and using the composite solution to satisfy boundary conditions is developed and rigorously followed to obtain a set of algebraic equations for the problem of inclination change with minimum energy loss. Repeated solution of these algebraic equations along the trajectory, treating each current state as an initial state, constitutes a feedback guidance algorithm. The solution is uniformly valid to zero order in an expansion parameter.