Differentials in Optimal Control

Abstract

In Chapter 2, it was shown that Taylor expansions of algebraic functions can be performed one term at a time by taking differentials. Once the differential process was defined, it was used from then on to obtain the first and second differentials associated with each parameter optimization problem. The purpose of this chapter is to extend the use of differentials to do Taylor expansions associated with the optimal control problem (Ref. Bl, p. 18). The elements of the optimal control problem are ordinary differential equations, algebraic final conditions, and integrals. In general, the first-order results of the Taylor expansion are used to define the differential operation, and their correctness is verified by deriving the second-order results by taking differentials.