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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, in 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'ouvrage
Date
1999
Book title
Stochastic and Differential Games. Theory and Numerical Methods
Book author
Bardi, Martino; Raghavan, T.E.S.; Parthasarathy, T.
Publisher
Springer
Published in
Berlin
ISBN
978-1-4612-7208-3
Number of pages
381
Pages
177-247
Publication identifier
http://dx.doi.org/10.1007/978-1-4612-1592-9_4
Metadata
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Author(s)
Cardaliaguet, Pierre
Quincampoix, Marc
Saint-Pierre, Patrick
Abstract (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.
Subjects / Keywords
Game theory

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