An extension of a stochastic control theorem due to Whittle

Whittle has obtained a theorem that gives the optimal control in terms of a mathematical expectation for the uncontrolled process for processes which are LQG except at termination. The type of cost function that he considered involves the state variable only at termination. In this paper we extend his result to the case when the cost function involves the state variable both at termination and along the way. We then apply our result to obtain the optimal control of the current in an electrical circuit.