Set-Valued Numerical Analysis for Optimal Control and Differential Games

  • Pierre Cardaliaguet
  • Marc Quincampoix
  • Patrick Saint-Pierre
Part of the Annals of the International Society of Dynamic Games book series (AISDG, volume 4)


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.


Closed Subset Differential Game Differential Inclusion Target Problem Viability Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Pierre Cardaliaguet
    • 1
    • 2
  • Marc Quincampoix
    • 1
    • 2
  • Patrick Saint-Pierre
    • 1
    • 2
  1. 1.Centre de Recherche ViabilitéJeux, ContrôleFrance
  2. 2.CNRS ERS 664University of ParisDauphineFrance

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