kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2026-23-2-12-25kaz29-2873Research ArticleМАТЕМАТИЧЕСКИЕ НАУКИMATHEMATICAL SCIENCESУПРАВЛЕНИЕ КВАЗИЛИНЕЙНЫМИ ИНТЕГРО-ДИФФЕРЕНЦИАЛЬНЫМИ СИСТЕМАМИ С ИМПУЛЬСНЫМ ВОЗДЕЙСТВИЕМCONTROL OF QUASILINEAR INTEGRO-DIFFERENTIAL SYSTEMS WITH IMPULSE EFFECTShttps://orcid.org/0000-0002-4666-8001СейловаР. Д.SeilovaR. D.

К.ф.-м.н., доцент.

Актобе

PhD, Associate Professor.

Aktobe

roza_seilova@mail.ruhttps://orcid.org/0000-0001-9728-8378ТалиповаМ. Ж.TalipovaM. Zh.

К.ф.-м.н., доцент.

Актобе

PhD, Associate Professor.

Aktobe

mira_talipova@mail.ruhttps://orcid.org/0000-0002-5847-9881БекбауоваА. У.BekbauovaA. U.

К.ф.-м.н., доцент.

Актобе

PhD, Associate Professor.

Aktobe

mirra478@mail.ruhttps://orcid.org/0000-0002-7352-5997ЕримбетоваГ. Г.YerimbetovaG. G.

Докторант.

Актобе

PhD student.

Aktobe

gulmira.yerimbetova1982@gmail.comАктюбинский региональный университет им. К. ЖубановаКазахстанK. Zhubanov Aktobe Regional UniversityKazakhstan2026270620262321225Copyright © Сейлова Р.Д., Талипова М.Ж., Бекбауова А.У., Еримбетова Г.Г., 20262026Сейлова Р.Д., Талипова М.Ж., Бекбауова А.У., Еримбетова Г.Г.Seilova R.D., Talipova M.Z., Bekbauova A.U., Yerimbetova G.G.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/2873

Современная теория управления активно расширяет границы исследований, выходя за рамки классических дифференциальных уравнений без особых воздействий. В данной статье рассматривается задача управляемости для квазилинейных интегро-дифференциальных систем с импульсным воздействием. Исследуется влияние слабых нелинейных возмущений, включенных в уравнения, определяющие моменты импульсного воздействия, что приводит к необходимости анализа систем с переменными моментами импульсов. Применяется метод сведения к уравнениям с фиксированными моментами импульсного воздействия, что позволяет использовать традиционные подходы к управлению. Разработаны методы построения разрешающего управления, обеспечивающего перевод системы из начального состояния в заданное конечное. Рассмотрены условия существования и единственности решений, а также оптимизация управления в среднем, направленная на минимизацию заданного функционала затрат. Полученные результаты могут быть применены в задачах автоматического регулирования, моделирования динамических систем с дискретными и непрерывными воздействиями, а также в управлении технологическими и экономическими процессами. Работа будет интересна для специалистов в области дифференциальных уравнений, теории управления и прикладной математики.

This paper examines the controllability problem of quasilinear integro-differential systems with impulse effects. The influence of weak nonlinear perturbations included in the equations that determine the moments of impulse effects is studied, leading to the necessity of analyzing systems with variable impulse moments. The method of reduction to equations with fixed impulse moments is applied, allowing for the use of classical control approaches. Methods for constructing admissible control that ensures the transition of the system from an initial state to a given final state are developed. The conditions for the existence and uniqueness of solutions, as well as the optimization of control in the mean, aimed at minimizing a given cost functional, are considered. The obtained results can be applied in automatic regulation tasks, modeling of dynamic systems with discrete and continuous influences, as well as in the control of technological and economic processes. This work will be of interest to specialists in differential equations, control theory, and applied mathematics.

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