Introduction

This chapter introduces the ideas behind optimization and optimal control and provides a brief history of calculus of variations and optimal control. The subject of optimization is quite general in the sense that it can be viewed in different ways depending on the approach the interest, the nature of the signals, and the stage used in optimization. optimization can be classified as static optimization and dynamic optimization. The main objective of optimal control is to determine control signals that will cause a process to satisfy some physical constraints and at the same time extremize a chosen performance criterion. Classical control design techniques have been successfully applied to linear, time-invariant, single-input, single output systems. The optimal control theory continues to have a wide variety of applications starting from the traditional electrical power to economics and management. The optimal control systems are studied in three stages. Finally, this chapter also provides an overview of this book.