mathematicsВестник российских университетов. МатематикаRussian Universities Reports. Mathematics2686-96672782-3342Тамбовский государственный университет имени Г.Р. Державина10.20310/2686-9667-2024-29-148-381-390mathematics-79Research ArticleСТАТЬИARTICLESО задачах импульсного управления, возникающих при разработке автоматизированных систем контроля численности вредителей в тепличных комплексахOn impulse control problems arising in automatization of pests control in greenhouseshttps://orcid.org/0000-0002-7286-9456БурлаковЕвгений ОлеговичBurlakovEvgenii O.eb_@bk.ruhttps://orcid.org/0009-0001-7784-6720ЯремаВиталий АлексеевичYaremaVitaly A.yaremavertal@mail.ruФГБУН «Институт проблем управления им. В. А. Трапезникова РАН»; ФГБОУ ВО «Тамбовский государственный университет им. Г. Р. Державина»; ФГАОУ ВО «Тюменский государственный университет»РоссияV. A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences; Derzhavin Tambov State University; Tyumen State UniversityRussian FederationФГАОУ ВО «Тюменский государственный университет»РоссияTyumen State UniversityRussian Federation20242512202429148381390Copyright © Бурлаков Е.О., Ярема В.А., 20242024Бурлаков Е.О., Ярема В.А.Burlakov E.O., Yarema V.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://mathematics.elpub.ru/jour/article/view/79

В работе предлагается математическая модель на основе непрерывной динамической системы, формализующая взаимодействие популяций насекомого-вредителя тепличной агрокультуры и энтомофага. В рамках модели энтомофаг, согласно концепции комплексной борьбы с вредителями, выступает агентом экологического контроля популяции насекомого-вредителя. Проводится идентификация параметров модели на основе экспериментальных данных, полученных в лабораторных условиях для тепличной системы «огурец обыкновенный — паутинный клещ — клещ-акарифаг». Для предложенной модели формулируется задача импульсного управления, отвечающая реализации контроля популяции вредителя при помощи энтомофага, исследуются вопросы существования решений и их непрерывной зависимости от управления. На основе исследованной управляемой системы обсуждаются вопросы построения экономически эффективных управляющих стратегий, позволяющих реализовывать востребованное при проектировании «умных» теплиц математическое обеспечение программно-аппаратных средств автоматизированных систем контроля численности вредителей.

The paper proposes a mathematical model based on a continuous dynamic system that formalizes the interaction of populations of a greenhouse agricultural insect pest and an entomophage acting as an agent of environmental control of the pest population in the framework of the concept of integrated pest management paradigm. The model parameters are identified based on experimental data obtained in laboratory conditions for the greenhouse system “cucumber — spider mite — acariphage mite”. For the proposed system, an impulse control problem that corresponds to the implementation of the pest population control using an entomophage is formulated, and the issues of the existence of solutions and their continuous dependence on control are investigated. Based on the studied control system, the issues of constructing cost-effective control strategies that allow implementing the mathematical software for automated pest control systems in greenhouses are discussed.

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