The task of controlling a given system of differential equations is ubiquitous in practice. Difficulties in obtaining an analytical solution determine the high demand for numerical methods. High relevance in solving particular problems is the construction of methods that take into account the specific structure of the problem. In this paper, we propose a method for reducing the UAV terminal control problem to a finite-dimensional nonlinear programming problem on coefficients of a certain type of polynomial with inequality-type restrictions. Increased attention is paid to guaranteed admissibility of the system trajectory and control, respectively. For this, we used the results of estimates of the range of values of the polynomial according to its representation in the form of Bernstein, which are asymptotically exact. Boundary conditions are taken into account using the Hermite polynomial.