Wiener system identification by input injection method

The article addresses the problem of nonlinear system identification with particular focusing on Wiener models. The proposed input injection methodology allows for identification of a working system-without stopping its usual operation, production processes, and so on. The only interferences are the slight random injections added to the input signal, which-by assumption-do not disturb the overall system's functionality. Such input injections allow to limit the curse of dimensionality issues, particularly troublesome in many approaches proposed in the literature for the Wiener system identification. Furthermore, all the requirements concerning the applicability of the method are rather mild. In particular, it is assumed that the static nonlinear characteristic is of nonparametric form and the existence of its two derivatives is needed for the consistency of the proposed estimate. The class of admissible output noises is also rather wide and does not exclude processes correlated with inputs signals.