Adaptation and robustness in predictive control

An explicit connection is made between the (nonadaptive) control law design stage of predictive adaptive control and techniques of linear-quadratic-Gaussian control with loop transfer recovery for robustness enhancement. The inherent controller design robustness of these methods is examined in terms of the nonadaptive closed-loop properties, that is of the class of open-loop perturbations to which the closed-loop system is robust, and of the effected input spectrum to the plant in closed loop. With this latter information, the authors then pose the question of to which plant model does the recursive least squares identification stage converge under this input. It is found that in many circumstances the identified model is precisely that which yields the best satisfaction of the previous robustness criterion for the control law. In this way, the authors demonstrate the robust interplay of the identifier and the controller in this class of adaptive control methods