Convexidade generalizada em problemas de controle ótimo com tempo livre
Ano de defesa: | 2014 |
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Autor(a) principal: | |
Orientador(a): | |
Banca de defesa: | |
Tipo de documento: | Dissertação |
Tipo de acesso: | Acesso aberto |
Idioma: | por |
Instituição de defesa: |
Universidade Estadual Paulista (Unesp)
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Programa de Pós-Graduação: |
Não Informado pela instituição
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Departamento: |
Não Informado pela instituição
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País: |
Não Informado pela instituição
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Palavras-chave em Português: | |
Link de acesso: | http://hdl.handle.net/11449/127565 http://www.athena.biblioteca.unesp.br/exlibris/bd/cathedra/31-08-2015/000843899.pdf |
Resumo: | In this work we study necessary and sufficient optimality conditions for free end-time optimal control problems, comprising the study of the Maximum Principle and generalized convexity. We introduce the necessary conditions of the xed end-time maximum principle and of the free end-time maximum principle. Next, we present sufficient conditions for xed end-time optimal control problems; we introduce two de nitions of generalized con- vexity, the rst called LMP-pseudoinvexity, which involves the Lagrange multipliers and the second called MP-pseudoinvexity, which does not involve the Lagrange multipliers. We show that for a LMP-pseudoinvex problem all the MP-processes (control processes that satisfy the necessary conditions of the maximum principle) are optimal processes and con- versely the problems such that all the MP-processes are optimal, are LMP-pseudoinvex problems; also we show that under some conditions, LMP-pseudoinvexity is equivalent to MP-pseudoinvexity. Finally, we present sufficient conditions for free end-time optimal control problem; we introduce a de nition of generalized convexity called MP-free pseudoinvexity, which does not involve the Lagrange multipliers. We show that under some conditions, if the problem is MP-free pseudoinvex, then all normal MP-processes are optimal; also we show that under some conditions, if the problem is such that every MP-process is an optimal process, then the problem is MP-free pseudoinvex |