The paper discusses optimal controls of processes with unknown constant parameters, where the processes are such that no measurements on the parameters are available during control periods. The general formulation of this optimal control problem is given for such systems, and it is shown that the formulation becomes quite simple when the equation for the observed-state vector is invertible, and that the problems of estimation and optimal controls cannot be separated for the class of problems discussed in the paper even when the systems are linear with quadratic criterion functions.