The aim of this book is to show that the nonparametric regression can be applied successfully to nonlinear system identification. It gathers what has been done in the area so far and presents main ideas, results, and some new recent developments.

The study of nonparametric regression estimation began with works published by Cencov, Watson, and Nadaraya in the 1960s. The history of nonparametric regression in system identification began about ten years later. Such methods have been applied to the identification of composite systems consisting of nonlinear memoryless systems and linear dynamic ones. Therefore, the approach is strictly connected with so-called block-oriented methods developed since Narendra and Gallman's work published in 1966. Hammerstein and Wiener structures are most popular and have received the greatest attention in numerous applications. Fundamental for nonparametric methods is the observation that the unknown characteristic of the nonlinear subsystem or its inverse can be represented as regression functions.

In terms of the a priori information, standard identification methods and algorithms work when it is parametric, that is, when our knowledge about the system is rather large; for example, when we know that the nonlinear subsystem has a polynomial characteristic. In this book, the information is much smaller, nonparametric. The mentioned characteristic can be, for example, any integrable or bounded or, even, any Borel function.