Sufficient Optimality Conditions for Optimal Control Problems with State Constraints

• Autor(a) principal: Antunes de Oliveira, Valeriano [UNESP]
• Data de Publicação: 2019
• Outros Autores: Nunes Silva, Geraldo [UNESP]
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1080/01630563.2018.1562469; http://hdl.handle.net/11449/188723
• topic: Generalized convexity; optimal control; state constraints; sufficient optimality conditions

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.