Thus far we have examined block-oriented systems of the cascade form, namely the Hammerstein and Wiener systems. The main tool that was used to recover the characteristics of the systems was based on the theory of nonparametric regression and correlation analysis. In this chapter, we show that this approach can be successfully extended to a class of block-oriented systems of the series-parallel form as well as systems with nonlinear dynamics. The latter case includes generalized Hammerstein and Wiener models as well as the sandwich system. We highlight some of these systems and present identification algorithms that can use various nonparametric regression estimates. In particular, Section 12.1 develops nonparametric algorithms for parallel, series-parallel, and generalized nonlinear block-oriented systems. Section 12.2 is devoted to a new class of nonlinear systems with nonlinear dynamics. This includes the important sandwich system as a special case.

Series-parallel, block-oriented systems

The cascade nonlinear systems presented in the previous chapters define the fundamental building blocks for defining general models of series-parallel forms. Together, all of these models may create a useful class of structures for modeling various physical processes. The choice of a particular model depends crucially on physical constraints and needs.

In this section, we present a number of nonlinear models of series-parallel forms for which we can relatively easily develop identification algorithms based on the regression approach used throughout the book.