
Set-Valued Numerical Analysis for Optimal Control and Differential Games
Cardaliaguet, Pierre; Quincampoix, Marc; Saint-Pierre, Patrick (1999), Set-Valued Numerical Analysis for Optimal Control and Differential Games, dans Bardi, Martino; Raghavan, T.E.S.; Parthasarathy, T., Stochastic and Differential Games. Theory and Numerical Methods, Springer : Berlin, p. 177-247. http://dx.doi.org/10.1007/978-1-4612-1592-9_4
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Type
Chapitre d'ouvrageDate
1999Titre de l'ouvrage
Stochastic and Differential Games. Theory and Numerical MethodsAuteurs de l’ouvrage
Bardi, Martino; Raghavan, T.E.S.; Parthasarathy, T.Éditeur
Springer
Ville d’édition
Berlin
Isbn
978-1-4612-7208-3
Nombre de pages
381Pages
177-247
Identifiant publication
Métadonnées
Afficher la notice complèteRésumé (EN)
This 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.Mots-clés
Game theoryPublications associées
Affichage des éléments liés par titre et auteur.
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Cardaliaguet, Pierre; Quincampoix, Marc; Saint-Pierre, Patrick (2000) Article accepté pour publication ou publié
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Quincampoix, Marc; Saint-Pierre, Patrick; Cardaliaguet, Pierre (2001) Article accepté pour publication ou publié
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