Worst-case ℒ1 identification using mixed parametric-nonparametric models

In this paper we study the problem of identifying a system within a given class, using input-output measurements corrupted by L_∞ bounded noise. The identification error is measured according to the L₁ norm of the impulse response, in the worst case with respect to allowable systems and noise. With nonparametric identification approach, the number of measurements needed to estimate n impulse response samples, within a given level of accuracy, grows exponentially with n, leading in most cases to unacceptable experimental conditions. In this paper we show that large improvements can be obtained with respect to the nonparametric approach by using more parsimonious classes of models, constituted of mixed parametric and nonparametric models