Abstract : In this research we continue our investigations of approximation techniques for a wide class of discrete and continuous time stochastic control problems. Emphasis is placed on the development and theoretical justification of techniques which yield computationally tractable algorithms that answer the following: (1) approximations to the optimal cost and the cost of using particular control; (2) approximations to the optimal control; (3) evaluation of the relative performance of two controls; and (4) estimates for the deterioration in system performance due to the failure to observe system components. (Author)