izvuzmathИзвестия высших учебных заведений. МатематикаIzvestiya Vysshikh Uchebnykh Zavedenii. Matematika0021-34462076-4626Казанский (Приволжский) федеральный университет10.26907/0021-3446-2024-8-3-19izvuzmath-96Research ArticleСтатьиИдентификация локальных изменений в динамике возрастной структуры населения при отсутствии начальных условийIdentification of the local changes in age-structured population dynamics with missing initial conditionАчабФ.AchabF.

Фатма Ачаб

г. Оум-Эль Буаги, 04000

Fatma Achab

Oum El Bouaghi, 04000

achab.fatma@univ-oeb.dzХафдаллаА.HafdallahA.

Абделхак Хафдалла

ул. Константина, г. Тебесса, 12002

Abdelhak Hafdallah

Constantine str., Tebessa, 12002

abdelhak.hafdallah@univ-tebessa.dzРеззоугИ.RezzougI.

Имад Реззоуг

г. Оум-Эль Буаги, 04000

Imad Rezzoug

Oum El Bouaghi, 04000

imadrezzoug@gmail.comУниверситет Ларби Бен МхидиАлжирUniversity of Larbi Ben MhidiAlgeriaУниверситет Шахида Шейха Ларби ТбессиАлжирEchahid Cheikh Larbi Tbessi UniversityAlgeria20243108202408319Copyright © Ачаб Ф., Хафдалла А., Реззоуг И., 20242024Ачаб Ф., Хафдалла А., Реззоуг И.Achab F., Hafdallah A., Rezzoug I.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://izvuzmath.elpub.ru/jour/article/view/96

Исследуется обратная задача, состоящая в определении неизвестных локальных изменений плотности населения, независимо от отсутствующей начальной возрастной структуры населения, на основе известных измерений состояния. Основная идея заключается в преобразовании исследования обратной задачи в задачу оптимального управления с неполными данными. Предложенный метод решения такого рода задач — это управление без сожалений, аппроксимированное последовательностью управлений с малым сожалением. Мы доказываем существование и единственность последовательности управлений с малым сожалением, которая слабо сходится к единственному управлению без сожалений. Локальные изменения будут охарактеризованы спаренной системой оптимальности.

In this paper, we study an inverse problem consisting of determining the unknown local changes of a population densities independent of the missing initial population age distribution from the knowledge of some measurement in the state. The main idea is to transform the study of the inverse problem into an optimal control problem with incomplete data. To solve this kind of problem, we use the method of no-regret control approximated by a sequence of low-regret control. We show the existence and uniqueness of the sequence of low-regret control, which converges weakly to the unique no-regret control. The local changes are characterized by a coupled optimality system.

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The authors declare that there are no conflicts of interest present.