2023 , Volume 28, № 5, p.55-69

Purpose. A multimethod approach for finding a numerical solution to the optimal control problem with phase constraints is constructed. The approach is adapted for solution of applied problems arising in various scientific and technical fields.

Methods. The developed approach is based on the reduction to a finite-dimensional optimization problem and constructively takes into account phase constraints by applying effective linear and nonlinear programming algorithms to solve auxiliary problems of a large dimension At the external iterations of this method, the problems of minimizing a specially constructed nonlinear functional (modified Lagrange function) are solved with phase constraints linearized on the obtained approxima- tion. The solution of these problems is found by the iterative method of the reduced gradient using a conjugate system for calculating gradients. Along with improving the control in this approach, the values of dual variables are simultaneously refined, through which the necessary optimality conditions are formed and the optimal control is calculated in the problem with phase constraints.

Findings. The software developed on the basis of the proposed approach and implementing the multi-method technique for calculating optimal control is successfully used to solve complex applied problems from various fields. The results of solving applied optimization problems of the electric power system and determining the optimal aircraft maneuver are presented.

Conclusions. Thus, the multimethod technology for solving the applied optimal control problems, implemented in the form of parallel iterative optimization processes with the choice of the best approximation, allows finding solution to the problem with the automatic application of different optimization methods and thereby significantly increases the efficiency of searching and reliability of obtaining the numerical solution with a given accuracy in applied optimal control problems.