Iterative upwind finite difference method with completed richardson extrapolation for state-constrained HJB equations

Abstract

In this work, we develop an iterative method in conjunction with an upwind finite difference discretization scheme for solving a Hamilton-Jacobi-Bellman (HJB) equation governing a class of state constrained optimal feedback control problems. We prove that the method is stable. We also propose an algorithm for computational domain reduction and a completed Richardson extrapolation technique to improve the accuracy of numerical solutions from the method. Numerical results will be presented to demonstrate the accuracy and efficiency of the method.