2026 , Volume 31, № 3, p.71-85

A development of the parametrization method for the numerical solution of optimal control problems is considered. The method employs dividing the time interval into a finite number of ntervals, each of which has a fixed control structure. The control structure is described by a finite number of parameters. In this case, the phase trajectory is completely determined by the control parameters and the interval nodes. This allows formulating a finite-dimensional nonlinear programming problem, the functions of which indirectly depend on the control parameters and the nodes of the interval. To apply effective methods of nonlinear programming, several schemes for calculating first- and second-order derivatives in the resulting finite-dimensional problem are proposed. The schemes contain three approaches to calculating derivatives: finite-difference approximation, direct calculation of phase trajectory variations by parameters, and calculation using a conjugate system. In the first two cases, parallel computing is used. At the same time, despite the fact that you have to solve more Cauchy problems than in the third case, gain time is expected. The results of the search for the optimal solution by the proposed schemes for three optimal control test problems are presented. Based on computational experiments, conclusions have been made on the applicability of the schemes, and a path for further research has been outlined.