Approximate solution of the Hamilton-Jacobi-Bellman equation

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.