On the value function for nonautonomous optimal control problems with infinite horizon

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dc.contributor.authorBaumeister, J.
dc.contributor.authorLeitao, A.
dc.contributor.authorSilva, Geraldo Nunes [UNESP]
dc.contributor.institutionUniversidade Federal de Santa Catarina (UFSC)
dc.contributor.institutionUniv Frankfurt
dc.contributor.institutionUniversidade Estadual Paulista (Unesp)
dc.date.accessioned2014-05-20T15:21:09Z
dc.date.available2014-05-20T15:21:09Z
dc.date.issued2007-03-01
dc.description.abstractIn this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.en
dc.description.affiliationUniv Fed Santa Catarina, Dept Math, BR-88040900 Florianopolis, SC, Brazil
dc.description.affiliationUniv Frankfurt, Dept Math, D-60054 Frankfurt A M, Germany
dc.description.affiliationUniv Estadual Paulista, Dept Comp Sci & Stat, BR-15054000 Sao Jose do Rio Preto, Brazil
dc.description.affiliationUnespUniv Estadual Paulista, Dept Comp Sci & Stat, BR-15054000 Sao Jose do Rio Preto, Brazil
dc.format.extent188-196
dc.identifierhttp://dx.doi.org/10.1016/j.sysconle.2006.08.011
dc.identifier.citationSystems & Control Letters. Amsterdam: Elsevier B.V., v. 56, n. 3, p. 188-196, 2007.
dc.identifier.doi10.1016/j.sysconle.2006.08.011
dc.identifier.issn0167-6911
dc.identifier.lattes3638688119433520
dc.identifier.urihttp://hdl.handle.net/11449/32329
dc.identifier.wosWOS:000244517800003
dc.language.isoeng
dc.publisherElsevier B.V.
dc.relation.ispartofSystems & Control Letters
dc.relation.ispartofjcr2.656
dc.relation.ispartofsjr1,939
dc.rights.accessRightsAcesso restrito
dc.sourceWeb of Science
dc.subjectdynamic programmingpt
dc.subjectinfinite horizonpt
dc.subjectviscosity solutionspt
dc.subjectDini solutionspt
dc.subjectexistencept
dc.titleOn the value function for nonautonomous optimal control problems with infinite horizonen
dc.typeArtigo
dcterms.licensehttp://www.elsevier.com/about/open-access/open-access-policies/article-posting-policy
dcterms.rightsHolderElsevier B.V.
unesp.author.lattes3638688119433520
unesp.author.orcid0000-0002-3574-9893[3]
unesp.campusUniversidade Estadual Paulista (Unesp), Instituto de Biociências Letras e Ciências Exatas, São José do Rio Pretopt

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