On The Pontryagin Maximum Principle For Optimal Control Problems

Abstract

The purpose of this thesis is to present a survey on the Pontryagin maximum principle. The main purpose of optimal control theory is to find an optimal control and its corresponding optimal trajectory. However, due to the hardness of finding an optimal solution of a given system directly, it is useful to use necessary conditions for optimal solutions. In this thesis, we introduce Pontryagin maximum principle for discrete and continuous systems and provide their proofs. We also find an optimal control for some specific examples with the necessary condition.