Formulation of the Control Problem

Abstract

In this chapter we first point out the common mathematical structure of the examples in the previous chapter. This permits a somewhat imprecise preliminary formulation of the mathematical problem of optimal control. It should, however, motivate the precise and more general formulation of the mathematical problem of optimal control which is given in Section 3. In Section 4 we discuss various equivalent formulations of the problem, and in Section 5 we show how some other control problems can be cast in the form given in Section 3. We conclude this chapter with a discussion of the relationship between problems in the calculus of variations and control problems. Sections 4 to 6 inclusive can be omitted at a first reading and can be read as the need arises.