Application of the dynamic programming method to obtain of the angular velocity control law of a spacecraft with a small geometric asymmetry in the atmosphere

Abstract

The atmospheric descent of a spacecraft with a small geometric asymmetry is considered. A quasi-linear dynamic system describes the motion of a spacecraft relative to the center of mass. The aim of the paper is to obtain the approximate optimal angular velocity control law, taking into account the change of the geometric asymmetry. We apply the method of dynamic programming and the non-resonant scheme of the averaging method for the synthesis of the optimal control law. Numerical results confirm the effectiveness of the obtained approximate law for optimal control of the angular velocity with respect to the problem of descent of the spacecraft with a small geometric asymmetry in the Martian atmosphere.