Approximate solution of the Hamilton-Jacobi-Bellman equation

سال انتشار: 1401
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 27

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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.

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