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Numerical Schemes for Discontinuous Value Functions of Optimal Control

Cardaliaguet, Pierre; Quincampoix, Marc; Saint-Pierre, Patrick (2000), Numerical Schemes for Discontinuous Value Functions of Optimal Control, Set-Valued Analysis, 8, 1-2, p. 111-126. http://dx.doi.org/10.1023/A:1008774508738

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Type
Article accepté pour publication ou publié
Date
2000
Journal name
Set-Valued Analysis
Volume
8
Number
1-2
Publisher
Springer
Pages
111-126
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
Quincampoix, Marc
Saint-Pierre, Patrick
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.
Subjects / Keywords
viability; optimal control; value function