Identification of block-oriented nonlinear systems starting from linear approximations: A survey

TL;DR

This survey reviews methods for identifying block-oriented nonlinear systems starting from linear approximations, highlighting frameworks like the best linear approximation and epsilon-approximation that aid in model initialization and selection.

Contribution

It provides a comprehensive overview of how linear approximations are used to identify block-oriented nonlinear models and discusses various algorithms and frameworks involved.

Findings

Linear approximations effectively initialize nonlinear system identification.

Frameworks like the best linear approximation guide model structure selection.

Survey covers diverse approaches and highlights key methodologies.

Abstract

Block-oriented nonlinear models are popular in nonlinear system identification because of their advantages of being simple to understand and easy to use. Many different identification approaches were developed over the years to estimate the parameters of a wide range of block-oriented nonlinear models. One class of these approaches uses linear approximations to initialize the identification algorithm. The best linear approximation framework and the $\epsilon$-approximation framework, or equivalent frameworks, allow the user to extract important information about the system, guide the user in selecting good candidate model structures and orders, and prove to be a good starting point for nonlinear system identification algorithms. This paper gives an overview of the different block-oriented nonlinear models that can be identified using linear approximations, and of the identification algorithms that have been developed in the past. A non-exhaustive overview of the most important other block-oriented nonlinear system identification approaches is also provided throughout this paper.