Through optimization of branching injection trajectories by the Pontryagin maximum principle using stochasticmodels

A problem of the through optimization of aerospace vehicle branching ascent trajectories in view of atmospheric disturbances (wind and thermodynamic parameters variations) and constraints on admissible areas of separated parts fall points is considered. The problem solution is based on the Pontryagin maximum principle. The problem with a continuum of branches corresponding random disturbances was reduced to the more standard one with a finite set of branches being the most critical (at the given event probability) with regard to the functional considered. The analytical synthesis of such critical disturbances profiles is obtained on basis of the Bliss formula, connecting a functional change with variations of right parts of motion equations. The developed technique and its efficiency are demonstrated by an example for a typical launcher.