The use of optimization techniques for the control of drives using a frequency controlled induction motor as an actuator is considered. The approach proposed is based on the choice of a specific control law in the framework of a prefixed class of stabilizing feedback controls. The optimized performance index is obtained aposterioriby applying the Bellmann's principle to a problem with an index in which the term depending on the state is initially unspecified. Successively, the control law is developed, and it is proved how it minimizes a particular index which takes into account both the influence of the error and the control effort. This index has proved very useful in the control choice since it makes it possible to determine a correspondence between the elements of the weighting matrices and the system transient behaviour.