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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 | ||
آمار تعداد مشاهده مقاله: 1,281 تعداد دریافت فایل اصل مقاله: 1,512 |