Free Boundary Value Problems and HJB Equations for the Stochastic Optimal Control of Elasto-Plastic Oscillators

M. LAURIERE; Z. LI; L. MERTZ; J. WYLIE; S. ZUO

doi:10.1051/proc/201965425

Free Boundary Value Problems and HJB Equations for the Stochastic Optimal Control of Elasto-Plastic Oscillators

M. LAURIERE, Z. LI, L. MERTZ, J. WYLIE, S. ZUO

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

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Abstract

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. © EDP Sciences, SMAI 2019.

Original language	English
Pages (from-to)	425-444
Journal	ESAIM: Proceedings and Surveys
Volume	65
DOIs	https://doi.org/10.1051/proc/201965425
Publication status	Published - Feb 2019

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GRF: Dynamics of Noise-Driven Inelastic Particle Systems
WYLIE, J. J. (Principal Investigator / Project Coordinator) & Mertz, L. (Co-Investigator)
1/01/16 → 25/05/20
Project: Research

Cite this

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title = "Free Boundary Value Problems and HJB Equations for the Stochastic Optimal Control of Elasto-Plastic Oscillators",

abstract = "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{\textquoteright}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. {\textcopyright} EDP Sciences, SMAI 2019.",

author = "M. LAURIERE and Z. LI and L. MERTZ and J. WYLIE and S. ZUO",

year = "2019",

month = feb,

doi = "10.1051/proc/201965425",

language = "English",

volume = "65",

pages = "425--444",

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TY - JOUR

T1 - Free Boundary Value Problems and HJB Equations for the Stochastic Optimal Control of Elasto-Plastic Oscillators

AU - LAURIERE, M.

AU - LI, Z.

AU - MERTZ, L.

AU - WYLIE, J.

AU - ZUO, S.

PY - 2019/2

Y1 - 2019/2

N2 - 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. © EDP Sciences, SMAI 2019.

AB - 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. © EDP Sciences, SMAI 2019.

U2 - 10.1051/proc/201965425

DO - 10.1051/proc/201965425

M3 - RGC 21 - Publication in refereed journal

VL - 65

SP - 425

EP - 444

JO - ESAIM: Proceedings and Surveys

JF - ESAIM: Proceedings and Surveys

ER -

Free Boundary Value Problems and HJB Equations for the Stochastic Optimal Control of Elasto-Plastic Oscillators

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GRF: Dynamics of Noise-Driven Inelastic Particle Systems

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