Identification and Control: Joint Input Design and H∞ State Feedback with Ellipsoidal Parametric Uncertainty

One obstacle in connecting robust control with models generated from prediction error identification is that very few control design methods are able to directly cope with the ellipsoidal parametric uncertainty regions that are generated by such identification methods. In this contribution we present a sufficient condition for the existence of a H
∞
state feedback controller for the multi-input/single-output case which accomodates for ellipsoidal parametric uncertainty. The condition takes the form of a linear matrix inequality whose solution also provides a set of valid feedback gains. The model class considered corresponds to systems with known poles but uncertain zero locations. A second important contribution of the paper is to integrate the input design problem in system identification with this control synthesis method. This means that given H
∞
specifications on the closed loop transfer function are translated into the requirements on the input signal spectrum used to identify the process so that the ellipsoidal model uncertainty resulting from model identification using this input spectrum will be shaped such that the control specifications are satisfied for all models in the uncertainty set and hence guaranteed for the true system. The procedures are illustrated on a numerical example.