Optimal control and guidance for vehicles gaining altitude under the aerodynamical conditions

Abstract

At the ascent path for the space plane with the air breathing engines and the large wings, the optimal steering law indicates sinusoidal behavior in contrast to a conventional law for rockets. The first primary result of this paper is the analytical description of this periodic behavior emerged from the optimal steering. It concludes that a conventional linear tangent law is applicable only to non-lift vehicles. Then the numerical analysis of the optimal control law with the state constraint is achieved by DCNLP method. In addition, the paper proposes two kind of the new guidance schemes to compensate the flight path error aroused by the disturbance. The first one is the way to approximate the optimal steering using the trigonometric function form and the second one is the way to get the control variable substituting the approximate expression of the dynamics derived from the result of the optimal steering into the equation of motion. These guidance schemes have only a few parameters to be determined and are easily obtained to keep maximizing the terminal horizontal speed by the consumption of a few percentage fuel margins. Show more