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

*Iraqi Journal of Science*

2008, Volume 49, Issue 1, Pages 178-187

2008, Volume 49, Issue 1, Pages 178-187

#### 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.

#### Keywords

Lagrange problem, optimal control, Hamilton - Jacobi equation, dynamic programming, dual value function, Bolza problem.#### Metrics