dc.contributor.author Frankowska, Halina dc.date.accessioned 2014-10-30T12:51:39Z dc.date.available 2014-10-30T12:51:39Z dc.date.issued 1987 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/14079 dc.language.iso en en dc.subject Differential equations en dc.subject Viscosity en dc.subject Optimal control en dc.subject.ddc 515 en dc.title Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equation en dc.type Communication / Conférence dc.description.abstracten In 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.citationpages 727-732 en dc.relation.ispartoftitle 26th IEEE Conference on Decision and Control, 1987. Proceedings en dc.relation.ispartofpublname IEEE en dc.relation.ispartofdate 1987 dc.subject.ddclabel Analyse en dc.relation.conftitle 26th IEEE Conference on Decision and Control, 1987 en dc.relation.confdate 1987-12 dc.relation.confcity Los Angeles en dc.relation.confcountry États-Unis en dc.relation.forthcoming non en dc.identifier.doi http://dx.doi.org/10.1109/CDC.1987.272464 en
﻿

## Files in this item

FilesSizeFormatView

There are no files associated with this item.