E.V. Antipina, S.A. Mustafina, A.F. Antipin. Evolutionary algorithms for finding approximate solutions to optimal control problems ... P. 21-31

Optimal control problems with terminal constraints and with a free right end of the trajectory are considered. Each of the problems is approximated by a finite-dimensional problem. The control is subject to a constraint and is defined in the class of piecewise constant functions. Numerical algorithms are formulated to find approximate solutions to the problems. The iterative algorithms are based on the differential evolution method. A feature of the proposed approach is that the solution found is independent of the choice of the initial approximation. The results of numerical experiments on solving optimal control problems are presented. For each problem, a suboptimal control and the corresponding trajectory of the process are calculated. The results obtained are compared with solutions found by gradient methods. The comparison proves the effectiveness of using the developed evolutionary algorithms for solving optimal control problems.

Keywords: optimal control problem, differential evolution, terminal constraints, evolutionary calculations

Received August 5, 2023

Revised September 26, 2023

Accepted October 7, 2023

Funding Agency: This work was supported by the Ministry of Science and Higher Education of the Russian Federation (code FZWU-2023-0002).

Evgenia Viktorovna Antipina, Cand. Phys.-Math. Sci., Ufa University of Science and Technology, Ufa, 450076 Russia, e-mail: stepashinaev@ya.ru

Svetlana Anatolyevna Mustafina, Dr. Phys.-Math. Sci., Prof., Ufa University of Science and Technology, Ufa, 450076 Russia, e-mail: mustafina_sa@mail.ru

Andrey Fedorovich Antipin, Cand. Techn. Sci., Sterlitamak Branch of Ufa University of Science and Technology, Sterlitamak, 453103 Russia, e-mail: andrejantipin@ya.ru


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Cite this article as: E.V. Antipina, S.A. Mustafina, A.F. Antipin. Evolutionary algorithms for finding approximate solutions to optimal control problems. Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2024, vol. 30, no. 1, pp. 21–31.