Solving the optimal control problem using a nonlinear programming technique. II - Optimal Shuttle ascent trajectories

The optimal control for the second stage of the Space Shuttle ascent has been determined using a nonlinear programming method. The optimality conditions for such a problem are implicit in the control for a general representation of the aerodynamic data. Since the optimality conditions of this problem could not be solved explicitly for the control, a differential-algebraic integrator was required. The problem was first solved using an approximation of the aerodynamic data in a special form. This approximation produced optimality conditions that could be explicitly solved for the control, allowing the use of a fast, standard integrator. A comparison of the optimal control solution with the linear tangent solution was made for several cases of 'yaw steering'. The phrase 'yaw steering' refers to changes, after staging, in desired final inclination or right ascension of the ascending node (terminal constraints). Linear tangent steering yields a final weight within a few pounds of the optimal control weight.