Worst-Case Identification of Errors-in-Variables Models in Closed Loop

A worst-case identification method in frequency domain is proposed to cope with the identification of errors-in-variables models (EIVMs) in closed loop. With a priori bound for the disturbing noises of an EIVM in closed loop, a frequency-domain normalized coprime factor model (NCFM) with perturbation is derived and thus the identification of the EIVM becomes that of the NCFM. By employing the v-gap metric as an optimization criterion, the worst-case error for an identified nominal NCFM is easily quantified and the parameter optimization can be effectively solved by linear matrix inequalities (LMIs). During the parameter optimization, the derivative of the nominal NCFM is constrained to some degree to reduce the effect of overfitting phenomenon. Different from other EIVM identification methods, we use v-gap metric to characterize the disturbing noises and quantify the worst-case error for the nominal NCFM. As a result, the identification result is not a deterministic model but a model set. Moreover, this model set can be perfectly combined with the robust controller design. Finally, a numerical simulation is presented to verify the proposed method.