Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators
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...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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EDP Sciences
2019-01-01
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| Series: | ESAIM: Proceedings and Surveys |
| Online Access: | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196518.pdf |
| _version_ | 1797968403057606656 |
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| author | Lauriere M. Li Z. Mertz L. Wylie J. Zuo S. |
| author_facet | Lauriere M. Li Z. Mertz L. Wylie J. Zuo S. |
| author_sort | Lauriere M. |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-11T02:45:15Z |
| format | Article |
| id | doaj.art-36237c1a9c4244a4a21cb4e9f7104e9c |
| institution | Directory Open Access Journal |
| issn | 2267-3059 |
| language | English |
| last_indexed | 2024-04-11T02:45:15Z |
| publishDate | 2019-01-01 |
| publisher | EDP Sciences |
| record_format | Article |
| series | ESAIM: Proceedings and Surveys |
| spelling | doaj.art-36237c1a9c4244a4a21cb4e9f7104e9c2023-01-02T17:57:56ZengEDP SciencesESAIM: Proceedings and Surveys2267-30592019-01-016542544410.1051/proc/201965425proc196518Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillatorsLauriere M.Li Z.Mertz L.Wylie J.Zuo S.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.https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196518.pdf |
| spellingShingle | Lauriere M. Li Z. Mertz L. Wylie J. Zuo S. Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators ESAIM: Proceedings and Surveys |
| title | Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators |
| title_full | Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators |
| title_fullStr | Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators |
| title_full_unstemmed | Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators |
| title_short | Free boundary value problems and hjb equations for the stochastic optimal control of elasto-plastic oscillators |
| title_sort | free boundary value problems and hjb equations for the stochastic optimal control of elasto plastic oscillators |
| url | https://www.esaim-proc.org/articles/proc/pdf/2019/01/proc196518.pdf |
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