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The purpose of the scientific research, results are determinated in the article, is to analytically synthesize the control law of an unmanned aerial vehicle while guiding one along the trajectory that specified by the reference points of space in an inertial coordinate system. The analysis of various existing approaches of the formation of a given flight path of an unmanned aerial vehicle based on various mathematical formulations of the problem is carried out. To achieve the goal, the flight path is considered as separate intervals, where the control optimization problem is solved. The optimization criterion in general form is substantiated and its presentation in the form of a minimized quadratic quality functional is convenient for analytical control synthesis. As components of the functional, the parameters of the deviation of the flight path of the aircraft from the specified points of space are considered, as well as the predicted parameters of the velocity vector and the control normal acceleration. Moreover, at each specified point in space, the direction of the trajectory to the subsequent point is taken into account, that ensures optimal curvature of the trajectory by specified flight speed of the unmanned aerial vehicle. As a result of analytical synthesis, mathematical dependences are obtained to determine control acceleration, which allow us to get a specified optimal control law on board an unmanned aerial vehicle, which ultimately ensures minimum energy consumption. The validity of the proposed theoretical provisions is confirmed by a clear example, where for a simplified mathematical problem statement the optimal laws of change in control acceleration and the trajectory parameters of an unmanned aerial vehicle are calculated by computer simulation.