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dc.contributor.authorFrankowska, Halina
dc.date.accessioned2014-10-30T12:51:39Z
dc.date.available2014-10-30T12:51:39Z
dc.date.issued1987
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14079
dc.language.isoenen
dc.subjectDifferential equationsen
dc.subjectViscosityen
dc.subjectOptimal controlen
dc.subject.ddc515en
dc.titleOptimal trajectories associated to a solution of contingent Hamilton-Jacobi equationen
dc.typeCommunication / Conférence
dc.description.abstractenIn this paper we study the existence of optimal trajectories associated with a generalized solution to Hamilton-Jacobi-Bellman equation arising in optimal control. In general, we cannot expect such solutions to be differentiable. But, in a way analogous to the use of distributions in PDE, we replace the usual derivatives with "contingent epiderivatives" and the Hamilton-Jacobi equation by two "contingent Hamilton-Jacobi inequalities". We show that the value function of an optimal control problem verifies these "contingent inequalities". Our approach allows the following three results: (a) The upper semicontinuous solutions to contingent inequalities are monotone along the trajectories of the dynamical system. (b) With every continuous solution V of the contingent inequalities, we can associate an optimal trajectory along which V is constant. (c) For such solutions, we can construct optimal trajectories through the corresponding optimal feedback. They are also "viscosity solutions" of a Hamilton-Jacobi equation. Finally we discuss the link of viscosity solutions with Clarke's approach to the Hamilton-Jacobi equation.en
dc.identifier.citationpages727-732en
dc.relation.ispartoftitle26th IEEE Conference on Decision and Control, 1987. Proceedingsen
dc.relation.ispartofpublnameIEEEen
dc.relation.ispartofdate1987
dc.subject.ddclabelAnalyseen
dc.relation.conftitle26th IEEE Conference on Decision and Control, 1987en
dc.relation.confdate1987-12
dc.relation.confcityLos Angelesen
dc.relation.confcountryÉtats-Unisen
dc.relation.forthcomingnonen
dc.identifier.doihttp://dx.doi.org/10.1109/CDC.1987.272464en


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