dc.contributor.author Tahraoui, Rabah dc.contributor.author Carlier, Guillaume dc.date.accessioned 2010-02-25T08:36:09Z dc.date.available 2010-02-25T08:36:09Z dc.date.issued 2010 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/3572 dc.language.iso en en dc.subject Hamilton-Jacobi-Bellman equations in infinite dimensions en dc.subject Dynamic programming en dc.subject state equations with memory en dc.subject viscosity solutions en dc.subject.ddc 519 en dc.title Hamilton-Jacobi-Bellman equations for the optimal control of a state equation with memory en dc.type Article accepté pour publication ou publié dc.description.abstracten This 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: en $v(x,z):=\inf_{u\in V} \left\{ \int_0^{+\infty} e^{-\lambda s } L(y_{x,z,u}(s), u(s))ds \right\}$ 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. dc.relation.isversionofjnlname ESAIM. COCV dc.relation.isversionofjnlvol 16 dc.relation.isversionofjnlissue 3 dc.relation.isversionofjnldate 2010 dc.relation.isversionofjnlpages 744-763 dc.relation.isversionofdoi http://dx.doi.org/10.1051/cocv/2009024 en dc.identifier.urlsite http://hal.archives-ouvertes.fr/hal-00363273/en/ en dc.description.sponsorshipprivate oui en dc.relation.isversionofjnlpublisher EDP Sciences en dc.subject.ddclabel Probabilités et mathématiques appliquées en
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