Introduction. The solution to the problem on the centroidal motion control synthesis (guidance problem) of an unmanned aerial vehicle (UAV) with long-range capabilities in the boost phase is considered. Control condition requires optimum fuel consumption. The principle of dynamic programming considering the restrictions to the vector modulus of the thrust output is used to solve the problem. The implementation of terminal guidance requires the formation of control as a function of the object state at the end of the ascent phase. The attainment of these boundary conditions determines the further transition to the ballistic flight phase.Materials and Methods. Bellman’s principle of dynamic programming is the most reasonable from the point of view of the implementability of the computationally efficient on-board algorithms and the solution to the problems in the form of synthesis. With natural scarcity of thrust and energy resources on board, this principle enables to obtain solutions free from the switching functions. In this case, the optimal control is a smooth function (without derivative discontinuity) of the current and final parameters of the UAV.Research Results. A new algorithmic method for the synthesis of terminal motion control is developed. Its difference is that the UAV movement control in the ascent phase is formed by the function of the motion actual and terminal parameters. This ensures movement along an energetically optimal trajectory into the given region of space. The problem solution results enable to build closed terminal guidance algorithms for the boost phase of the UAV trajectory with long-range capabilities. Such algorithms have good convergence and injection accuracy due to the prediction of parameters during the flight at a shorter time interval.Discussion and Conclusions. The most preferred is the principle of dynamic programming. It should be used when solving the problem on the centroidal motion control synthesis (guidance problem) of the UAV with long-range capabilities in the boost phase.