The entire work has been devided into two parts. The methods of nonstandard analysis are applied to deterministic control theory extending earlier work by the author, in Part I. Compactness of relaxed controls, continuity of solution and cost as functions of the controls, and existence of optimal controls are included in the established results. The methods are extended to obtain similar results for partially observed stochastic control in Part II. The feedback control involved in the systems considered depends on information from a digital read-out of the observation process. The noise in the state equation is controlled along with the drift. Similar methods are applied to a Markov system in the final section of the paper. The presentation of the contents is nice.