Adaptive control of diffusion processes with a discounted reward criterion

. The optimal control problem we are dealing with in this paper is to determine control policies that maximize a discounted reward criterion when the dynamic system evolves as a stochastic differential equation (SDE). Both the instantaneous reward function and the SDE’s drift coef-ficient may depend on an unknown parameter. We give conditions ensur-ing the existence of an asymptotically optimal policy using the so-called Principle of Estimation and Control. We illustrate our results with several examples.