The Optimal Control Problem

Abstract

In this chapter we shall discuss an optimization problem that we will call “the optimal control problem.” In the 1950’s, motivated especially by aerospace problems, engineers became interested in the problem of controlling a system governed by a set of differential equations. In many of the problems it was natural to want to control the system so that a given performance index would be minimized. In some aerospace problems large savings in cost could be obtained with a small improvement in performance so that optimal operation became very important. As techniques were developed which were practical for computation and implementation of optimal controls the use of this theory became common in a large number of fields. References which illustrate work typical in applying optimal control to economic problems are Burmeister-Döbell [1], Pindyck [1], Shell [1].