Optimal Angle of Attack Control for Aerocapture Maneuvers

Recent investigations of aerocapture maneuvers have considered direct force control as a
promising alternative to bank angle control. By modulating the angle of attack and sideslip
angle independently, the longitudinal and lateral channels can be decoupled and thus solved
separately. However, the optimal angle of attack profile for minimizing post-atmospheric
propellant expenditure was previously unknown. This research applies principles of optimal
control theory to numerically solve for the optimal angle of attack profile for control of the
longitudinal channel. Direct methods are first employed to discretize the angle of attack profile
and show that an optimal solution follows a nearly bang-bang (full lift up then full lift down)
structure under a variety of conditions along the flight path angle corridor. To corroborate
these results, indirect methods were also applied to scope the Optimal Control Problem (OCP)
as a Two Point Boundary Value Problem (2P-BVP) which could then be solved numerically. The
indirect optimization results aligned closely with the direct results, providing further evidence
that a bang-bang structure provides a good approximation for the optimal angle of attack
profile for aerocapture maneuvers using direct force control.