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dc.contributor.authorTahraoui, Rabah
dc.contributor.authorCarlier, Guillaume
dc.date.accessioned2010-02-25T08:36:09Z
dc.date.available2010-02-25T08:36:09Z
dc.date.issued2010
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3572
dc.language.isoenen
dc.subjectHamilton-Jacobi-Bellman equations in infinite dimensionsen
dc.subjectDynamic programmingen
dc.subjectstate equations with memoryen
dc.subjectviscosity solutionsen
dc.subject.ddc519en
dc.titleHamilton-Jacobi-Bellman equations for the optimal control of a state equation with memoryen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis article is devoted to the optimal control of state equations with memory of the form: ?[x(t) = F\left(x(t),u(t), \int_0^{+\infty} A(s) x(t-s) ds\right), \; t>0, with initial conditions x(0)=x, \; x(-s)=z(s), s>0.]Denoting by $y_{x,z,u}$ the solution of the previous Cauchy problem and: \[v(x,z):=\inf_{u\in V} \left\{ \int_0^{+\infty} e^{-\lambda s } L(y_{x,z,u}(s), u(s))ds \right\}\] where $V$ is a class of admissible controls, we prove that $v$ is the only viscosity solution of an Hamilton-Jacobi-Bellman equation of the form: \[\lambda v(x,z)+H(x,z,\nabla_x v(x,z))+\=0\] in the sense of the theory of viscosity solutions in infinite-dimensions of M. Crandall and P.-L. Lions.en
dc.relation.isversionofjnlnameESAIM. COCV
dc.relation.isversionofjnlvol16
dc.relation.isversionofjnlissue3
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages744-763
dc.relation.isversionofdoihttp://dx.doi.org/10.1051/cocv/2009024en
dc.identifier.urlsitehttp://hal.archives-ouvertes.fr/hal-00363273/en/en
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherEDP Sciencesen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen


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