Time optimal control in a problem of launcher injection

Questions of optimal control construction in a problem of injecting a rocket carrier (a launcher) into a given circumglobal elliptic orbit are considered. An optimization problem consists in designing a program control for launcher that provides the maximal value of the payload mass led to the given orbit. The motion of the launcher is described by a nonlinear dynamic system. There are some additional requirements on a desired control and they generate constraints on the phase state of the dynamic system. In the framework of the mathematical model of the problem of maximizing the payload mass led to the orbit is equivalent to the optimal time problem with terminal constraints [1]. The realization of common approaches to this problem solution is connected with essential computational difficulties. An algorithm for approximate solving of this problem is developed in [2]. This algorithm is based on the original problem decomposition to several optimal control problems. Here, the quasi-optimal control is a result of specialized iterative procedure. The approaches to solving some optimal time problems with phase constraints are discussed.
1. T.D.Dumsheva, V.B.Kostousov, E.K.Kostousova, V.I.Pochinskii On a problem of optimal putting a payload into a given elliptic orbit // Proceedings of Institute of Mathematics and Mechanics UB RAS, 2010. V.16. №5.p.57-65. 2. D.V.Mazgalin, V.I.Pochinsky The method of determining the azimuth of the start and the tangage angle program on the active site of atmospheric flight of rocket launcher // Vestnik SUSU. Series “Computer technologies, control and radio electronics”. 2010. issue 12. No 22(198). p.47-50.