[Inéquations de Hamilton–Jacobi–Bellman de deuxième ordre]
Cette note est consacrée à l'étude des inéquations aux dérivées partielles du type Hamilton–Jacobi–Bellman issues d'un problème de contrôle optimal où l'équation d'état est une inéquation variationnelle stochastique. En fait, on démontre que la fonction minimisant la fonctionnelle de coût est une solution de viscosité pour l'équation étudiée. Cette approche est menée par une méthode de perturbation du problème initial. L'unicité de la solution de viscosité est également prouvée.
This work is devoted to the study of a class of Hamilton–Jacobi–Bellman inequalities which come from an optimal control problem where the state equation is a stochastic variational inequality. We show that the value function, which minimizes the cost, is a viscosity solution of the studied equation. This approach is made by perturbing the initial problem. Then we prove the uniqueness of the inequality.
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@article{CRMATH_2002__335_7_591_0,
author = {Z\u{a}linescu, Adrian},
title = {Second order {Hamilton{\textendash}Jacobi{\textendash}Bellman} inequalities},
journal = {Comptes Rendus. Math\'ematique},
pages = {591--596},
publisher = {Elsevier},
volume = {335},
number = {7},
year = {2002},
doi = {10.1016/S1631-073X(02)02528-1},
language = {en},
url = {https://www.numdam.org/articles/10.1016/S1631-073X(02)02528-1/}
}
TY - JOUR AU - Zălinescu, Adrian TI - Second order Hamilton–Jacobi–Bellman inequalities JO - Comptes Rendus. Mathématique PY - 2002 SP - 591 EP - 596 VL - 335 IS - 7 PB - Elsevier UR - https://www.numdam.org/articles/10.1016/S1631-073X(02)02528-1/ DO - 10.1016/S1631-073X(02)02528-1 LA - en ID - CRMATH_2002__335_7_591_0 ER -
%0 Journal Article %A Zălinescu, Adrian %T Second order Hamilton–Jacobi–Bellman inequalities %J Comptes Rendus. Mathématique %D 2002 %P 591-596 %V 335 %N 7 %I Elsevier %U https://www.numdam.org/articles/10.1016/S1631-073X(02)02528-1/ %R 10.1016/S1631-073X(02)02528-1 %G en %F CRMATH_2002__335_7_591_0
Zălinescu, Adrian. Second order Hamilton–Jacobi–Bellman inequalities. Comptes Rendus. Mathématique, Tome 335 (2002) no. 7, pp. 591-596. doi : 10.1016/S1631-073X(02)02528-1. https://www.numdam.org/articles/10.1016/S1631-073X(02)02528-1/
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