Approximate solution of the Hamilton-Jacobi-Bellman equation

Document Type : Research Paper

Authors

1 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

2 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

3 Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran & The Center of Excellence on Modeling and Control Systems (CEMCS), Mashhad, Iran

10.22124/jmm.2021.18386.1579

Abstract

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.

Keywords