Об одном оптимальном управлении нелинейнойсистемой дробного порядка в локально выпукломпространстве
Об одном оптимальном управлении в локально выпуклом пространстве
DOI:
https://doi.org/10.56143/ee30r795Ключевые слова:
уравнение дробного порядка, локально выпуклое пространство, функция Понтрягина, метод последовательных приближений, сжимающее отображение, существование, единственность, устойчивость.Аннотация
В данной работе рассматривается задача оптимального управления для системы нелинейных интегро-дифференциальных уравнений дробного порядка в локально выпуклом пространстве. Функция Понтрягина строится на основе введения сопряжённой финальной задачи. Посредством дифференцирования этой функции по функции управления получается интегральное уравнение относительно управления. С использованием семейства полунорм, задающих топологию локально выпуклого пространства, а также условий равномерной ограниченности и липшицевости для заданных нелинейных отображений, метод последовательных приближений сочетается с принципом сжимающих отображений. Доказываются существование и единственность функции управления и соответствующей функции состояния, а также непрерывная зависимость функции состояния от начального элемента.
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