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Numerical Schemes for Discontinuous Value Functions of Optimal Control

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Date
2000
Dewey
Probabilités et mathématiques appliquées
Sujet
viability; optimal control; value function
Journal issue
Set-Valued Analysis
Volume
8
Number
1-2
Publication date
2000
Article pages
111-126
Publisher
Springer
DOI
http://dx.doi.org/10.1023/A:1008774508738
URI
https://basepub.dauphine.fr/handle/123456789/6896
Collections
  • CEREMADE : Publications
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Author
Cardaliaguet, Pierre
Quincampoix, Marc
Saint-Pierre, Patrick
Type
Article accepté pour publication ou publié
Abstract (EN)
In this paper we explain that various (possibly discontinuous) value functions for optimal control problem under state-constraints can be approached by a sequence of value functions for suitable discretized systems. The key- point of this approach is the characterization of epigraphs of the value functions as suitable viability kernels. We provide new results for estimation of the convergence rate of numerical schemes and discuss conditions for the convergence of discrete optimal controls to the optimal control for the initial problem.

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