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This paper deals with a joint input-output method of identifying a closed-loop Hammerstein-Wiener system, where a linear plant in the forward loop may be unstable. A model that simulates the closed-loop system is derived using basis function expansions of nonlinearities. First, a linear state-space model of the forward loop is identified using Two-stage ORT method [12]1. Then, initialized by the identified state-space model and linear approximations of nonlinearities, the joint input-output mean square error (MSE) is optimized by using the robust gradient method [20]; the identification algorithm yields good numerical results within moderate computation time.

A Joint Input-Output Approach to Closed-loop Identification of Hammerstein-Wiener Systems