The Relationship between Dynamic Programming and Pontryagin's Minimum principle in Optimal Control

Abstract

    Optimal control theory has been used to obtain solutions to a variety

of aerospace engineering problems and holds great promise for other problem areas as well. However, much remains to be accomplished. Hopefully, the reader has been stimulated to learn more about optimal control theory and its applications. In this paper, we discussed the relationship between dynamic programming and Pontryagin's minimum principle and the important features of these two techniques.

     The minimum principle determines optimal controls that generally lead to a nonlinear two-point boundary deriving the minimum principle from the Hamilton Jacobi-Bellman functional equation. Particular problem solved with applying minimum principle technique and has been discussed. The minimum principle indicated that the only values assumed determined by an optimal control.