V A Sesyukalov (Moscow Aviation Institute (National Research University)) :


Articles:

629.7 Modeling of the control structure based on a discrete Bellman principal applied to problems with special controls

Sesyukalov V. A. (Moscow Aviation Institute (National Research University))


doi: 10.18698/2309-3684-2026-1-321


The purpose of this article is to obtain control structures in problems of dynamic object control. The control structure in this work is called regular and special (in the sense of the maximum principle) control sections leading to the solution of the transport problem. The paper presents an algorithm for determining the control structure based on the Bellman optimality principle for an additive quality criterion. The algorithm is proposed for use at the initial stages of the study to determine the first approximation. The algorithm involves searching for control, including transfer time, in the considered phase region on a grid of phase parameters. The Bellman function is approximated using a piecewise linear television involute. Methods for projecting the phase coordinate to the nearest "least" node number in the involute and back, from a known involute node number to the corresponding phase coordinate are also given. The algorithm is then applied to the problem of the fastest ascent of an aircraft (a time-optimal problem) containing special control extremals. The solutions obtained under the appliance of the proposed algorithm are given, and some efforts has been made to obtained similar trajectories within appliance of the maximum principle. The presented algorithm, in general, showed satisfying convergence to solutions according to the maximum principle, satisfying the conditions of the transport problem. However, it was not possible to satisfy all the necessary optimality conditions for the structures obtained by the algorithm. Merits of algorithm are acquiring of high variety of trajectories, parallel processing, easy consideration of phase constraints.


Сесюкалов В.А. Моделирование структуры управления на основе дискретного принципа Беллмана в задачах с особым управлением. Математическое моделирование и численные методы, 2026, № 1, с. 3–21.