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Optimal Control of Insect Populations

Author

Listed:
  • Anderson L. Albuquerque de Araujo

    (Departamento de Matemática, Universidade Federal de Viçosa, Viçosa 36570-000, Brazil
    These authors contributed equally to this work.)

  • José L. Boldrini

    (Departamento de Sistemas Integrados, Faculdade de Engenharia Mecânica, Universidade Estadual de Campinas, Campinas 13083-970, Brazil
    These authors contributed equally to this work.)

  • Roberto C. Cabrales

    (Instituto de Investigación Multidisciplinaria en Ciencia y Tecnología, Universidad de la Serena, La Serena 1720256, Chile
    These authors contributed equally to this work.)

  • Enrique Fernández-Cara

    (Departamento de Ecuaciones Diferenciales y Análisis Numérico e IMUS, Universidad de Sevilla, 41004 Sevilla, Spain
    These authors contributed equally to this work.)

  • Milton L. Oliveira

    (Departamento de Matemática, Universidade Federal da Paraíba, João Pessoa 58051-900, Brazil
    These authors contributed equally to this work.)

Abstract

We consider some optimal control problems for systems governed by linear parabolic PDEs with local controls that can move along the domain region Ω 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.

Suggested Citation

  • Anderson L. Albuquerque de Araujo & José L. Boldrini & Roberto C. Cabrales & Enrique Fernández-Cara & Milton L. Oliveira, 2021. "Optimal Control of Insect Populations," Mathematics, MDPI, vol. 9(15), pages 1-25, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1762-:d:601601
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