ON THE EXISTENCE OF THE SOLUTION TO THE HAMILTON- JACOBI EQUATION BY USING THE DUAL DYNAMICAL PROGRAMMING

Abstract

Properties of the value function and dual value function for an optimal control problems of Lagrange and Bolza are described. A main theorem is proved, this theorem deals with the existence of a maximum solution to the Hamilton-Jacobi equation for the Lagrange problem, with satisfies the Lipschitz condition by using the dual dynamic programming method. Finally gives an example which illustrates the value of the main theorem.