AN INTRODUCTION TO MATHEMATICAL OPTIMAL CONTROL THEORY

Abstract

In control theory, we are interested in governing the state of a system by using controls. One can explain Optimal Control Theory as the science of maximizing the returns and minimizing the costs of the operation of physical, social, and economic processes. In this work, we are devoted to study the controllability and the existence of optimal control of linear first order ordinary differential equations. And then, we study the Pontryagin Maximum Principle which helps us to characterize the optimal control. In this work, our main aim is to study the existence of optimal control, the Pontryagin Maximum Principle and its various applications.