Stochastic optimal control and its connection with estimation

The paper describes a formulation of the stochastic control problem in which the primary and secondary performance indices are distinguished. A minimisation and averaging principle, defining the connection between the two indices, is established, and some conclusions resulting from the principle are described. The generalised certainty equivalence principle, in some new notation, is also presented. Finally, the original generalised recursive estimation problem, which is equivalent to the stochastic optimal control problem, is formulated and solved.