Controllability Investigations of a Two-Stage-To-Orbit Vehicle

For the real-time computation of closed-loop controls, guidance methods have been recently developed by the authors which are based on the theory of neighboring extremals and/or the multiple shooting algorithm. Because of their close relationship, these methods have a comparable domain of controllability, i.e., the set of all deviations from the nominal optimal trajectory which can be compensated in real time. Therefore , the multiple shooting method can be used to get an estimation for the size of these domains. In this way, the domain of controllability has been investigated for the payload maximum ascent of a two-stage rocket-propelled space vehicle from Earth into a circular target orbit. Here, the staging and the mass ratio of the two stages are optimized simultaneously.