Репозитарій ОНУ імені І.І.Мечникова

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Approximation of solutions to the optimal control problem for the impulsive system with maximum
(Одеський національний університет імені І. І. Мечникова, 2016) Kichmarenko, Olha D.; Sapozhnikova, Katerina Yu.; Dashkovskiy, S.; Кічмаренко, Ольга Дмитрівна; Сапожнікова, Катерина Юріївна; Дашковський, С.; Кичмаренко, Ольга Дмитриевна; Сапожникова, Екатерина Юрьевна; Дашковский, С.
This paper presents the averaging method for two problems: impulsive system with maximum and for the optimal control problem of this kind of system. For the first problem the Krylov–Bogolyubov’s theorem is generalized. For the second one we are interested not only in approximation of the solution for optimal control problems with impulsive perturbation and maximum but also in approximation of corresponding functionals. In this purpose the averaging method is obtained as well. In this case averaging scheme includes the algorithm of correspondence between control functions of original and averaged optimal control problems. A numerical-asymptotic algorithm for solving an optimal control problem with a small parameter of such kind of system is designed.