Journal of Mathematical Modeling, Volume (10), No (1), Year (2021-6) , Pages (1-21)

Title : ( Approximate solution of the Hamilton-Jacobi-Bellman equation )

Authors: Atefeh Gooran Orimi , Sohrab Effati , Mohammad Hadi Farahi ,

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The Hamilton-Jacobi-Bellman (HJB) equation, as a notable approach obtained from dynamic programming, is widely used in solving optimal control problems that results in a feedback control law. In this study, the HJB equation is first transformed into the Convection-Diffusion (CD) equation by adding aviscosity coefficient. Then, a novel numerical method is presented to solve the corresponding CD equation and to obtain a viscosity solution of the HJB. The proposed approach encompasses two well-known methods of Finite Volume Method (FVM) and Algebraic Multigrid (AMG). The former as a reliable method for solving parabolic PDEs and the latter as a powerful tool for acceleration. Finally, numerical examples illustrate the practical performance of the proposed approach.


, Optimal control problems, Hamilton-Jacobi-Bellman (HJB) equation, convection-diffusion equation, finite volume method, algebraic multigrid method
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author = {Gooran Orimi, Atefeh and Effati, Sohrab and Farahi, Mohammad Hadi},
title = {Approximate solution of the Hamilton-Jacobi-Bellman equation},
journal = {Journal of Mathematical Modeling},
year = {2021},
volume = {10},
number = {1},
month = {June},
issn = {2345-394X},
pages = {1--21},
numpages = {20},
keywords = {Optimal control problems; Hamilton-Jacobi-Bellman (HJB) equation; convection-diffusion equation;finite volume method; algebraic multigrid method},


%0 Journal Article
%T Approximate solution of the Hamilton-Jacobi-Bellman equation
%A Gooran Orimi, Atefeh
%A Effati, Sohrab
%A Farahi, Mohammad Hadi
%J Journal of Mathematical Modeling
%@ 2345-394X
%D 2021