Approximate solution of the Hamilton-Jacobi-Bellman equation
محل انتشار: مجله مدلسازی ریاضی، دوره: 10، شماره: 1
سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 31
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شناسه ملی سند علمی:
JR_JMMO-10-1_006
تاریخ نمایه سازی: 19 خرداد 1403
چکیده مقاله:
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.
کلیدواژه ها:
نویسندگان
Atefeh Gooran Orimi
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran
Sohrab Effati
Department 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
Mohammad Hadi Farahi
Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran & The Center of Excellence on Modeling and Control Systems (CEMCS), Mashhad, Iran