ЗАДАЧА ОПТИМАЛЬНОГО КЕРУВАННЯ ДЛЯ ОДНОВИМІРНОГО НЕЛІНІЙНОГО РІВНЯННЯ ШРЕДІНГЕРА З СПЕЦІАЛЬНИМ ГРАДІЄНТНИМ ДОДАНКОМ
DOI:
https://doi.org/10.17721/2706-9699.2019.2.06Ключові слова:
задача оптимального керування, рівняння ШредінгераАнотація
У даній роботі розглянуто задачу оптимального керування для одновимірного нелінійного керування Шредінгера з спеціальним градієнтним доданком з комплексним коефіцієнтом у нелінійній частині, коли критерій якості є фінальним функціоналом та керування є квадратично сумовними функціями. При цьому було досліджено питання коректності постановки та необхідних умов оптимальності для розв’язків даної задачі оптимального керування. Доведено теорему існування та єдиності розв’язку та встановлено необхідні умови оптимальності у вигляді варіаційної нерівності. Також знайдено формулу для градієнта критерія якості.
Посилання
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