The adaptive control design problem for a discrete time system with structured parameteric uncertainty, which minimizes its weighted predicted output uncertainty is addressed in this article. A measure of the system uncertainty is quantified through the application of the set-membership (SM) identification scheme. The SM-estimator identifies a parallelepiped within which the system parameter vector is located. For a given future input sequence, this parameter uncertainty induces an uncertainty in the predicted system output. The control objective is to derive the input sequence that minimizes the predicted output uncertainty while tracking a reference input. Simulation studies are presented to highlight the features of the proposed control scheme.