Minimax approach to trajectory optimization of multistage launch vehicles

An optimum pitch steering program is developed, using a minimax technique, for a multistage launch vehicle in the presence of large parameter uncertainties. The uncertainties are characterized by deterministic bounds on the respective parameters. The pitch steering program is obtained by maximizing two independent scalar performance indexes. (1) the coast apogee velocity for a specified altitude; (2) the perigee of the satellite orbit. The product of dynamic pressure and angle of attack is constrained so as to minimize the structural loads during the atmospheric flight. The values of the uncertain parameters are determined by minimizing the same performance indexes in order to achieve a worst case design. The existence of saddle point solution to this class of problems is shown using the techniques of differential game theory. The conjugate gradient algorithm has been used for computer aided design of the minimax technique.