Universal regulators for optimal tracking in discrete-time systems affected by harmonic disturbances

Considers the problem of controlling a discrete-time linear system by output feedback so as to have a second output z_t track an observed reference signal r_t. The authors turn to an approach to the tracking problem, which allows for damping of other system and control variables, and this is our main result. The measure of performance is given by a natural quadratic cost function. The object is to design an optimal regulator which is universal in the sense that it does not depend on the unknown amplitudes and phases of r_t and w_t and is optimal for all choices of r_t and w _t. The authors prove that an optimal universal regulator exists in a wide class of stabilizing and possibly nonlinear regulators under natural technical conditions and that this regulator is in fact linear, provided that the second dimensionality condition above is satisfied. On the other hand, if it is not satisfied, the existence of an optimal universal regulator is not a generic property, so as a rule no optimal universal regulator exists