| Issue |
ESAIM: ProcS
Volume 65, 2019
CEMRACS 2017 - Numerical methods for stochastic models: control, uncertainty quantification, mean-field
|
|
|---|---|---|
| Page(s) | 425 - 444 | |
| DOI | https://doi.org/10.1051/proc/201965425 | |
| Published online | 02 April 2019 | |
Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators
1
ORFE, Princeton University, Princeton, NJ 08540, USA
e-mail: lauriere@princeton.edu
2
ECNU-NYU Institute of Mathematical Sciences, NYU Shanghai, Shanghai, China
e-mail: laurent.mertz@nyu.edu ; zhehua.li@nyu.edu ; siyao.zuo@nyu.edu
3
Department of Mathematics, City University of Hong Kong, Hong Kong, China
e-mail: mawylie@cityu.edu.hk
We consider the optimal stopping and optimal control problems related to stochastic variational inequalities modeling elasto-plastic oscillators subject to random forcing. We formally derive the corresponding free boundary value problems and Hamilton-Jacobi-Bellman equations which belong to a class of nonlinear partial of differential equations with nonlocal Dirichlet boundary conditions. Then, we focus on solving numerically these equations by employing a combination of Howard’s algorithm and the numerical approach [A backward Kolmogorov equation approach to compute means, moments and correlations of non-smooth stochastic dynamical systems; Mertz, Stadler, Wylie; 2017] for this type of boundary conditions. Numerical experiments are given.
Résumé
Nous considérons les problèmes de l’arrˆet optimal et du contrôle optimal associés à des inéquations variationelles stochastiques modélisant des oscillateurs élasto-plastiques sous forçage aléatoire. Nous obtenons formellement les problèmes à frontière libre et les équations de Hamilton-Jacobi-Bellman correspondantes qui appartiennent à une classe d’équations aux dérivés partielles nonlinéaires avec des conditions aux bord de Dirichlet nonlocales. Ensuite, nous nous concentrons sur la résolution numérique de ces équations en employant une combinaison de l’algorithme d’Howard et de l’approche numérique [A backward Kolmogorov equation approach to compute means, moments and correlations of non-smooth stochastic dynamical systems; Mertz, Stadler, Wylie; 2017] pour ce type de conditions aux bord. Des expériences numériques sont présentés.
© EDP Sciences, SMAI 2019
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