Incerteza intervalar em otimização e controle

Detalhes bibliográficos
Ano de defesa: 2015
Autor(a) principal: Leal, Ulcilea Alves Severino [UNESP]
Orientador(a): Não Informado pela instituição
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Universidade Estadual Paulista (Unesp)
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://hdl.handle.net/11449/127927
Resumo: The purpose of this research is to look at interval uncertainty in optimization problems and control. We present a process to determine the solutions of interval-valued optimization problems. Using extremal differentiability, we demonstrate the necessary conditions and present the sufficient conditions for three different concepts of solutions. In this study, we formulated the problem of interval-valued optimal control and demonstrated the optimality of necessary and sufficient conditions using extremal differentiability and generalized Hukuhara differentiability under assumptions of convexity. Furthermore, we applied these results in the area of weed management and control with an intervalvalued objective function in order to describe the best and worst-case scenarios for crop profitability in corn. The results for the interval analysis theory were found according to single-level constraint interval arithmetic for both the interval-valued functions and the interval functions. We defined the concept of single-level integral and derivative for interval-valued functions and obtained the fundamental theorem of calculus for the interval context. Using this concept, we then analyzed interval ordinary differential equations and obtained the existence and uniqueness theorem of the solution. Considering that the interval functions developed were −single-level differentiable, we formulated the interval optimal control problem and demonstrated the necessary and sufficient optimality conditions under assumptions of convexity for the problem in question