Numerical methods for optimal control problems

Abstract

Abstract Although a great deal can be learnt from closed-form solutions of optimal control problems, in general the solution of such problems can only be obtained by computation. Some numerical methods that can be used to solve optimal control problems are discussed in this chapter. Since the time-optimal principle TOP derived in Part A provides a criterion for the optimal control that is identical to that derived from the PMP as applied to time-optimal problems (see §9.1), we need only discuss the way in which the PMP can be implemented in a numerical solution of a general optimal control problem. The development of appropriate algorithms for such problems is fraught with obstacles, and it does not seem possible to produce schemes that will apply in general. Each problem, or class of problems, has to be considered on its own; all that can be done here is to describe methods that work in some specific cases.