A NEW TYPE OF DISCRETE EULER-LAGRANGE EQUATION WITH APPLICATIONS IN OPTIMAL CONTROL

A new type of discrete Euler-Lagrange equation, suitable for generalization, is presented in this paper. Several forms of this equation can be found in references. They have different differential operators as well as combinations of them. The equation given in this paper uses only one differential operator providing easy generalizations of Euler-Lagrange equation. In the paper, generalizations for the case of more variables and more ordered differences in the functional which is optimized, are derived. The application in determining optimal control of a discrete system is also given