ON THE EXISTENCE OF THE SOLUTION TO THE HAMILTON- JACOBI EQUATION BY USING THE DUAL DYNAMICAL PROGRAMMING
Lagrange problem
optimal control
Hamilton dynamic programming
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.