
Chapter 1
Examples of Control Problems
1.1 Introduction
Control theory is a mathematical study of how to influence the behavior
of a dynamical system to a chieve a des ired goal. In optimal co ntrol, the goal
is to maximize or minimize the numerical value of a specified quantity that is
a function of the behavior of the system. Optimal control theory developed in
the latter half of the 20th century in response to diverse applied problems. In
this chapter we present examples of optimal control problems to illustrate the
diversity of applications, to raise some of the mathematical issues involved, and
to motivate the mathematical formulation in subsequent ...