Stochastic control for systems with an unknown parameter is considered in this paper. The underlying problem is to minimize a functional subject to a system described by a singularly perturbed differential equation with an unknown parameter process driven by fast fluctuating random disturbances. This problem arises in the context of stochastic adaptive control, adaptive signal processing, and failure-prone manufacturing systems. Due to the nature of the wide-bandwidth noise processes, identifying the parameter process for each t is very hard since the driving noise changes very rapidly. An alternative approach is used, and an auxiliary control problem is introduced to overcome the difficulties. By means of weak convergence methods and comparison control techniques, nearly optimal controls are obtained.