The Patchy Cost and Feedback for the HJB PDE

Abstract. In this paper, we describe our development of a higher-order method for solving the Hamilton-Jacobi-Bellman PDE by incorporating several techniques. There are the power series method of Albrecht, Cauchy-Kovalevskaya techniques, patchy methods of Ancona and Bressan and Navasca and Krener, the fast sweep-ing and marching methods, and regularization methods. We also demonstrate the method through an example.