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Error Estimates for Second Order Hamilton-Jacobi-Bellman Equations. Approximation of Probabilistic Reachable Sets

By Mohamed Assellaou, Olivier Bokanowski and Hasnaa Zidani

Abstract

International audienceThis work deals with numerical approximations of unbounded and discontinuous value functions associated to some stochastic control problems. We derive error estimates for monotone schemes based on a Semi-Lagrangian method (or more generally in the form of a Markov chain approximation). A motivation of this study consists in approximating chance-constrained reachability sets. The latters will be characterized as level sets of discontinuous value functions associated to adequate stochastic control problems. A precise analysis of the level-set approach is carried out and some numerical simulations are given to illustrate the approach

Topics: unbounded and discontinuous value function, Error estimates for HJB equations, level-set approach, stochastic reachability analysis, chance constraints, numerical approximation, [ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]
Publisher: HAL CCSD
Year: 2015
DOI identifier: 10.3934/dcds.2015.35.3933
OAI identifier: oai:HAL:hal-00998371v2
Provided by: Hal-Diderot

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