A discussion of dynamic programming and some of the closed form solutions which are derived along with a sample solution to a simple problem are used to introduce the method. Limitations and difficulties encountered using dynamic programming as a numerical technique are discussed before the investigation of methods for overcoming the difficulties are covered. The problem of finding optimal control for a thrusting vehicle is investigated using three approaches. First, the criterion of minimum squared terminal error with respect to a predetermined impact point is studied using polynomial approximation with Tchebicheff Polynomials to represent the return which is a function of three variables. Next, the minimum time intercept using a discrete return function representation is investigated. The return in this case is a function of two variables. Finally, a one dimensional stochastic problem is studied. The criterion chosen is the probability that the interceptor comes within a prescribed distance of the desired impact point.