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

Abstract : This 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.
Document type :
Journal articles
Complete list of metadatas

Cited literature [34 references]  Display  Hide  Download

https://hal.inria.fr/hal-00998371
Contributor : Hasnaa Zidani <>
Submitted on : Monday, July 27, 2015 - 7:35:25 PM
Last modification on : Wednesday, July 3, 2019 - 10:48:04 AM
Long-term archiving on : Wednesday, April 26, 2017 - 8:02:45 AM

File

ARTICLE-Hal.pdf
Files produced by the author(s)

Identifiers

Citation

Mohamed Assellaou, Olivier Bokanowski, Hasnaa Zidani. Error Estimates for Second Order Hamilton-Jacobi-Bellman Equations. Approximation of Probabilistic Reachable Sets. Discrete and Continuous Dynamical Systems - Series A, American Institute of Mathematical Sciences, 2015, 35 (9), pp.3933 - 3964. ⟨10.3934/dcds.2015.35.3933⟩. ⟨hal-00998371v2⟩

Share

Metrics

Record views

795

Files downloads

812