On problems of putting a carrier rocket into specified elliptic orbits

We consider problems of an optimal program control of a carrier rocket of Soyuz-2 type aimed at placing a maximum mass of the carrier rocket into specified near-earth elliptic orbits and to a fixed point of an orbit as well as the problem of estimating the set of reachable points of an orbit. Numerical algorithms are developed for finding admissible controls. The algorithms are based on solving auxiliary problems of optimal control with the use of explicit formulas for parameters of the orbit and of the conjugate system. The question of the possibility of improving the base controls constructed at the Semikhatov Research and Production Association of Automation is investigated. As a result of extensive numerical modeling, it has been confirmed that the base controls are close to optimal ones and pointwise internal estimates for reachable sets have been found.