Min max feedback control of systems described by approximate models

The quadratic cost output regulators problem is considered for systems described by simplified linear models. By defining a suitable measure of the approximation between system and model, the problem is reduced to the control of the model with output affected by an error signal bounded by an input dependent constraint. A minmax approach is taken and both open loop and closed loop controls are studied and their relationships analyzed. It is shown that the feedback control cannot have a min max performance better than the open-loop one has, and a simple criterion is derived which points out when the min max performances for open loop and closed loop controls are equal.