This paper presents an upwind finite-difference method for the numerical approximation of viscosity solutions of a Hamilton-Jacobi-Bellman (HJB) equation governing a class of optimal feedback control problems. The method is based on an explicit finite-difference scheme, and it is shown that the method is stable under certain constraints on the step lengths of the discretization. Numerical results, performed to verify the usefulness of the method, show that the method gives accurate approximate solutions to both the control and the state variables.
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Wang et al. (2000) studied this question.