Introduction to Optimal Control Theory and Dynamical Systems

Abstract

The control theory and dynamical systems have been developed rapidly and they playing an ever more important role in linear and non-linear sciences and many applied fields during the past three decades . A lot of papers and number of books have been published in this area . But up to now , to our knowledge , it seems that there are only few books written by some mathematicians to expound the control theory and dynamical systems systematically .This is one of the main reasons why we have done this work . In this research, we investigate four applications of the optimal mathematical control theory problems, by analyzing four different mathematical models of dynamical systems. The research begins with chapter one as an introduction ,we provide a review of some basic concepts in control theory ,as well as the theory of optimal control and some definitions to be used later are concluded. In chapter two we defined the linear (nonlinear) systems and discussed fundamental theorems with some explanatory examples. Chapter three deals with a review of Reachability, Controllability, Observability and Sta- bility. In chapter four we discussed existence theorems for optimal control problems and static optimization with illustrated examples. The contribution of chapter five, is the main applications problems of this research which is a qualitative analytic study of mathematical models of control dynamical systems. Finally, we showed the maim conclusions.