Optimal Control of Insect Populations
We consider some optimal control problems for systems governed by linear parabolic PDEs with local controls that can move along the domain region <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo>&...
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MDPI AG
2021-07-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/15/1762 |
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| author | Anderson L. Albuquerque de Araujo José L. Boldrini Roberto C. Cabrales Enrique Fernández-Cara Milton L. Oliveira |
| author_facet | Anderson L. Albuquerque de Araujo José L. Boldrini Roberto C. Cabrales Enrique Fernández-Cara Milton L. Oliveira |
| author_sort | Anderson L. Albuquerque de Araujo |
| collection | DOAJ |
| description | We consider some optimal control problems for systems governed by linear parabolic PDEs with local controls that can move along the domain region <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> of the plane. We prove the existence of optimal paths and also deduce the first order necessary optimality conditions, using the Dubovitskii–Milyutin’s formalism, which leads to an iterative algorithm of the fixed-point kind. This problem may be considered as a model for the control of a mosquito population existing in a given region by using moving insecticide spreading devices. In this situation, an optimal control is any trajectory or path that must follow such spreading device in order to reduce the population as much as possible with a reasonable not too expensive strategy. We illustrate our results by presenting some numerical experiments. |
| first_indexed | 2024-03-10T09:12:32Z |
| format | Article |
| id | doaj.art-e42cc15a64dc4d1b8083d551d6050374 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T09:12:32Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-e42cc15a64dc4d1b8083d551d60503742023-11-22T05:56:17ZengMDPI AGMathematics2227-73902021-07-01915176210.3390/math9151762Optimal Control of Insect PopulationsAnderson L. Albuquerque de Araujo0José L. Boldrini1Roberto C. Cabrales2Enrique Fernández-Cara3Milton L. Oliveira4Departamento de Matemática, Universidade Federal de Viçosa, Viçosa 36570-000, BrazilDepartamento de Sistemas Integrados, Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, Campinas 13083-970, BrazilInstituto de Investigación Multidisciplinaria en Ciencia y Tecnología, Universidad de la Serena, La Serena 1720256, ChileDepartamento de Ecuaciones Diferenciales y Análisis Numérico e IMUS, Universidad de Sevilla, 41004 Sevilla, SpainDepartamento de Matemática, Universidade Federal da Paraíba, João Pessoa 58051-900, BrazilWe consider some optimal control problems for systems governed by linear parabolic PDEs with local controls that can move along the domain region <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mo>Ω</mo></semantics></math></inline-formula> of the plane. We prove the existence of optimal paths and also deduce the first order necessary optimality conditions, using the Dubovitskii–Milyutin’s formalism, which leads to an iterative algorithm of the fixed-point kind. This problem may be considered as a model for the control of a mosquito population existing in a given region by using moving insecticide spreading devices. In this situation, an optimal control is any trajectory or path that must follow such spreading device in order to reduce the population as much as possible with a reasonable not too expensive strategy. We illustrate our results by presenting some numerical experiments.https://www.mdpi.com/2227-7390/9/15/1762optimal controloptimality conditionsDubovitskii–Milyutin formalismcomputation of optimal solutions |
| spellingShingle | Anderson L. Albuquerque de Araujo José L. Boldrini Roberto C. Cabrales Enrique Fernández-Cara Milton L. Oliveira Optimal Control of Insect Populations Mathematics optimal control optimality conditions Dubovitskii–Milyutin formalism computation of optimal solutions |
| title | Optimal Control of Insect Populations |
| title_full | Optimal Control of Insect Populations |
| title_fullStr | Optimal Control of Insect Populations |
| title_full_unstemmed | Optimal Control of Insect Populations |
| title_short | Optimal Control of Insect Populations |
| title_sort | optimal control of insect populations |
| topic | optimal control optimality conditions Dubovitskii–Milyutin formalism computation of optimal solutions |
| url | https://www.mdpi.com/2227-7390/9/15/1762 |
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