Sufficient Optimality Conditions for Optimal Control Problems with State Constraints

It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum princip...

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Detalles Bibliográficos
Autores: Antunes de Oliveira, Valeriano [UNESP], Nunes Silva, Geraldo [UNESP]
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2019
País:Brasil
Institución:Universidade Estadual Paulista (UNESP)
Repositorio:Repositório Institucional da UNESP
Idioma:inglés
OAI Identifier:oai:repositorio.unesp.br:11449/188723
Acceso en línea:http://dx.doi.org/10.1080/01630563.2018.1562469
http://hdl.handle.net/11449/188723
Access Level:acceso abierto
Palabra clave:Generalized convexity
optimal control
state constraints
sufficient optimality conditions
Descripción
Sumario:It is well-known in optimal control theory that the maximum principle, in general, furnishes only necessary optimality conditions for an admissible process to be an optimal one. It is also well-known that if a process satisfies the maximum principle in a problem with convex data, the maximum principle turns to be likewise a sufficient condition. Here an invexity type condition for state constrained optimal control problems is defined and shown to be a sufficient optimality condition. Further, it is demonstrated that all optimal control problems where all extremal processes are optimal necessarily obey this invexity condition. Thus optimal control problems which satisfy such a condition constitute the most general class of problems where the maximum principle becomes automatically a set of sufficient optimality conditions.