Estudo da dinâmica de populações utilizando a técnica de polinômios de colocação

• Autor(a) principal: Resende, Ranulfo Acir de Oliveira [UNESP]
• Data de Publicação: 2015
• Tipo de documento: Dissertação
• Idioma: por
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://hdl.handle.net/11449/132672; http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/15-12-2015/000855212.pdf
• topic: Dengue; Matemática; Modelagem de dados; Metodos de simulação; Otimização combinatoria

This work comprises the study of a control system in its most simple format, that is, a controller and a process oer a plant. The optmization of a cost function, with the system state as variables, aims to achieve the optimal control. Starting from the concepts presented in the previous works, we studied alternatives optimization techniques suited to the optmal control. We used as experimental basement a mathemtical model of dengue disease's transmission, the same model adopted by some researchers to help to assess the best strategies to vanish the fertilized females, an index that is direclty related to the illness cases, as function of the relative costs of each technique available to combat the disease: the use of insecticides and the release of sterile males to the environment. The original researches that studies the same problem approached the matter by the formulation of an optimal control problem solved by Pontryagin Maximum Principle, in a sequential and approximated procedure. Others adopted genetic algorithm and multi-objective optimization. This research shows the results of the approach by dynamic optimization with collocation points in a integrated enviornment with modeling and simulation, JModelica, and optimization, IPOPT, tools. The application of the dynamic optimization with collocation points technique to the studied model allowed, by better observation of control signals and the assessment of the cost function, to suggest changes to a more efficient control