System Identification for H ∞ -Robust Control Design

Abstract

Conventional identification techniques are based on stochastic assumptions and yield minimum variance estimates. A major drawback of these techniques is that disturbances as well as model- uncertainties are treated as additive noise and are thus minimized together. Consequently hardly any indication of model-error bounds can be given, whereas robust control theory is based upon a nominal model together with both norm-bounded model-uncertainties and noise characterised in the frequency domain. It is our goal to present a new identification method using H ∞ -norms which yields a nominal model and information about the model-uncertainties applicable to H ∞ -robust control design. In the proposed method disturbances and noise signals at the input and output of the system are characterized as norm-bounded. The first step in the identification method is to compute uncertainty regions for the process dynamics in the complex plane. The a priori knowledge about the norm-bounds on the disturbances and properties of conformal mappings are used to compute these regions. The second step is to find a model in a model-set that minimizes the H ∞ -norm of the model errors, given the uncertainty regions. The first elementary implementation of the method is presented with two simulation studies.