Synthesis of the Optimal Control of the Spacecraft Orientation Using Combined Criteria of Quality

Abstract

The dynamic problem of a spacecraft’s (SC) rotation from an arbitrary initial angular position to a given final angular position is considered and solved. The case is investigated when the control is limited, and the minimized functional combines, in a given, proportion, the time of the maneuver and the integral of the energy of rotation. The construction of the optimal control is based on the quaternionic differential equation relating the vector of the angular momentum of the SC with the quaternion of the orientation of the body-related coordinate system. The control law is formulated in the form of an explicit dependence of the control variables on the phase coordinates. The analysis of the special control regime of the SC is carried out. Based on the conditions of transversality, as the necessary conditions for optimality, the optimal value of the kinetic energy of rotation when moving in a special control regime is determined. The created control algorithms allow turning of an SC with a kinetic rotation energy, which does exceed a predetermined level. For a dynamically symmetric SC, the problem of spatial reorientation is solved completely. The results of the mathematical modeling of the motion of an SC under the optimal control are presented, demonstrating the practical feasibility of the developed algorithm for controlling the spatial orientation of the SC.