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Gooran Orimi, Atefeh, Effati, Sohrab, Farahi, Mohammad Hadi. (1400). Approximate solution of the Hamilton-Jacobi-Bellman equation. فیزیولوژی و بیوتکنولوژی آبزیان, 10(1), 71-91. doi: 10.22124/jmm.2021.18386.1579
Atefeh Gooran Orimi; Sohrab Effati; Mohammad Hadi Farahi. "Approximate solution of the Hamilton-Jacobi-Bellman equation". فیزیولوژی و بیوتکنولوژی آبزیان, 10, 1, 1400, 71-91. doi: 10.22124/jmm.2021.18386.1579
Gooran Orimi, Atefeh, Effati, Sohrab, Farahi, Mohammad Hadi. (1400). 'Approximate solution of the Hamilton-Jacobi-Bellman equation', فیزیولوژی و بیوتکنولوژی آبزیان, 10(1), pp. 71-91. doi: 10.22124/jmm.2021.18386.1579
Gooran Orimi, Atefeh, Effati, Sohrab, Farahi, Mohammad Hadi. Approximate solution of the Hamilton-Jacobi-Bellman equation. فیزیولوژی و بیوتکنولوژی آبزیان, 1400; 10(1): 71-91. doi: 10.22124/jmm.2021.18386.1579

Approximate solution of the Hamilton-Jacobi-Bellman equation

Journal of Mathematical Modeling
دوره 10، شماره 1، فروردین 2022، صفحه 71-91    اصل مقاله (1.15 M)
نوع مقاله: Research Article
شناسه دیجیتال (DOI): 10.22124/jmm.2021.18386.1579
نویسندگان
Atefeh Gooran Orimi1؛ Sohrab Effati* 2؛ Mohammad Hadi Farahi3
1Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
2Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran & Center of Excellence of Soft Computing and Intelligent Information Processing (SCIIP), Ferdowsi University of Mashhad, Mashhad, Iran
3Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran & The Center of Excellence on Modeling and Control Systems (CEMCS), Mashhad, Iran
چکیده
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 a viscosity 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.
کلیدواژه‌ها
Optimal control problems؛ Hamilton-Jacobi-Bellman (HJB) equation؛ convection-diffusion equation؛ finite volume method؛ algebraic multigrid method
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