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dc.contributor.authorCardaliaguet, Pierre
dc.contributor.authorQuincampoix, Marc
dc.contributor.authorSaint-Pierre, Patrick
dc.date.accessioned2014-01-16T08:59:13Z
dc.date.available2014-01-16T08:59:13Z
dc.date.issued1999
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/12447
dc.language.isoenen
dc.subjectGame theoryen
dc.subject.ddc519en
dc.titleSet-Valued Numerical Analysis for Optimal Control and Differential Gamesen
dc.typeChapitre d'ouvrage
dc.description.abstractenThis chapter deals with theoretical and numerical results for solving qualitative and quantitative control and differential game problems. These questions are treated in the framework of set-valued analysis and viability theory. In a way, this approach is rather well adapted to look at these several problems with a unified point of view. The idea is to characterize the value function as a viability kernel instead of solving a Hamilton—Jacobi—Bellmann equation. This allows us to easily take into account state constraints without any controllability assumptions on the dynamic, neither at the boundary of targets, nor at the boundary of the constraint set. In the case of two-player differential games, the value function is characterized as a discriminating kernel. This allows dealing with a large class of systems with minimal regularity and convexity assumptions. Rigorous proofs of the convergence, including irregular cases, and completely explicit algorithms are provided.en
dc.identifier.citationpages177-247en
dc.relation.ispartoftitleStochastic and Differential Games. Theory and Numerical Methodsen
dc.relation.ispartofeditorBardi, Martino
dc.relation.ispartofeditorRaghavan, T.E.S.
dc.relation.ispartofeditorParthasarathy, T.
dc.relation.ispartofpublnameSpringeren
dc.relation.ispartofpublcityBerlinen
dc.relation.ispartofdate1999
dc.relation.ispartofpages381en
dc.relation.ispartofurlhttp://dx.doi.org/10.1007/978-1-4612-1592-9en
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.ispartofisbn978-1-4612-7208-3en
dc.relation.forthcomingnonen
dc.identifier.doihttp://dx.doi.org/10.1007/978-1-4612-1592-9_4en


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