This work presents a control algorithm which incorporates a Reference Model Robust Adaptive Controller (RMRAC) and a Linear Quadratic Regulator based on Kalman Filtering (LQR(KF)) to obtain a high performance and robust control system. The adaptive portion of the controller deals with system uncertainties, while the optimum scheme, aided by a Kalman Filter, is designed to deal with harmonically related system disturbances. A proof of stability is presented in addition to a numerical example of the combined RMRAC - LQR(KF) controller to show the effectiveness of this new control approach.