Application of Complex Functional of Quality in Optimal Control ‎Of Spacecraft Motion

The problem of optimal control of the reorientation of a spacecraft as a solid body from an arbitrary initial ‎position into a prescribed final angular position is considered and solved. the case is ‎studied in detail when the ‎minimized index combines, in a given proportion, the integral of modulus of angular momentum and duration of ‎maneuver. it is proved that the accepted optimality ‎criterion guarantees the motion of a spacecraft with modulus of ‎angular momentum not exceeding the required value. formalized equations and expressions for the synthesis of ‎the optimal rotation program are obtained using quaternion models. it is shown that the optimal solution corresponds to the strategy “acceleration rotation with constant modulus of angular momentum‎braking”, the ‎angular momentum and the controling moment are perpendicular during optimal rotation between acceleration and ‎braking. on the basis of necessary optimality conditions, the ‎main properties, laws, and key characteristics ‎‎(parameters, constants, integrals of motion) of the ‎optimal solution of the control problem, including the turn time ‎and the maximum angular momentum for the optimal motion, are determined. an estimation of the influence of the ‎bounded ‎controling moment on the character of the optimal motion and on the indicators of quality is ‎made. the ‎construction of an optimal control program of rotation is based on the quaternion variables and pontryagin’s ‎maximum principle. the value of maximal angular momentum magnitude is calculated by condition of ‎transversality. the designed method is universal and invariant ‎relative to the moments of inertia. for dynamically ‎symmetric spacecraft, a complete solution of ‎the reorientation problem in closed form is presented. an example ‎and results of mathematical ‎modeling of the motion of a spacecraft under optimal control are presented, ‎demonstrating the ‎practical feasibility of the method for controlling spacecraft’s spatial orientation.