Some results about the optimal LQG tracking problem

The optimal LQG tracking problem is studied both for available and for unavailable state and reference, assuming that the last variable is the addition of a known deterministic component and of a random noise component. In both cases the optimal solution exists, is unique, and the optimal control is a suitable a ne function of the current state and reference variable (when they are available) or of the corresponding optimal estimates (when they are not available). The minimum cost function is expressed in closed form