One-shot set-membership identification of Wiener models with polynomial nonlinearities

Abstract In this paper we propose a novel approach for set-membership identification of Wiener models when the static output map is a polynomial nonlinearity which, in general, is not assumed to be invertible. Two different estimators are considered in the paper. A setvalued estimator for the computation of the so-called parameter uncertainty intervals and a pointwise estimator aimed at the minimization of the error between the output of the estimated system and the measured one (output error minimization). A unified approach based on the formulation of a suitable semialgebraic optimization problem is proposed for the solution of the considered estimation problems. The proposed approach, which takes to one-shot estimation of the parameters values of both the linear and the nonlinear block, overcomes the main limitations of the approaches already available in the literature for set-membership identification of Wiener models. More precisely, it is not needed anymore any restrictive assumption on the nonlinearity invertibility. Effectiveness of the proposed algorithm is shown by means of a simulation example.

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