  In this paper, closed-loop entry guidance in a randomly perturbed atmosphere,
using bank angle control, is posed as a stochastic optimal control problem. The
entry trajectory, as well as the closed-loop controls, are both modeled as
random processes with statistics determined by the entry dynamics, the entry
guidance, and the probabilistic structure of altitude-dependent atmospheric
density variations. The entry guidance, which is parameterized as a sequence of
linear feedback gains, is designed to steer the probability distribution of the
entry trajectories while satisfying bounds on the allowable control inputs and
on the maximum allowable state errors. Numerical simulations of a Mars entry
scenario demonstrate improved range targeting performance when using the
developed stochastic guidance scheme as compared to the existing Apollo final
phase algorithm.
