Subspace predictive control based on subspace identification is discussed for joint system identification and control design. This combination enables automatic tuning of the parameters in model predictive control and avoids many steps in the LQG-controller design. It is independent of any priori information of the controller. Considering the constrain conditions, an ellipsoid optimization algorithm is proposed to generate a sequence of ellipsoids with decreasing volume. An upper bound of the maximum number of possible iteration steps is derived. As an example of helicopter, efficiency of the proposed subspace predictive control strategy is realized.