Nonlinear Optimal Control Theory

Chapter 6

The Maximum Principle and S ome of

Its Applications

6.1 Introduction

In this chapter we state several versions of the maximum principle, corre-

sp onding to different hypothese s o n the data of the problem. We shall collec-

tively call ea ch of these results, “the maximum principle”, and shall use them

to characterize the optimal controls in several important classes of problems.

The proof of the maximum principle will be given in the next chapter.

In Section 6.2 we use a dynamic programming argument to derive the max-

imum principle for ordinary pr oblems. Although the arguments are elementary

and mathema tically correct, the assumptions made ...