Model selection approaches for non-linear system identification: a review

• Published in: International journal of systems science Vol. 39; no. 10; pp. 925 - 946
• Main Authors: Hong, X., Mitchell, R.J., Chen, S., Harris, C.J., Li, K., Irwin, G.W.
• Format: Journal Article
• Language: English
• Published: London Taylor & Francis Group 01.10.2008; Taylor & Francis
• Subjects: adaptive learning; Applied sciences; Artificial intelligence; Computer science; control theory; systems; control engineering; Control theory. Systems; cross validation; Exact sciences and technology; Learning and adaptive systems; model generalisation; model selection; Modelling and identification; system identification; Availability; Bayes estimation; Non linear control; model selection; Cross validation; Modeling; adaptive learning; model generalisation; Kernels; Experimental design; Non linear model; Vector support machine; System identification; Learning algorithm; Convex analysis; control engineering
• ISSN: 0020-7721; 1464-5319
• DOI: 10.1080/00207720802083018

The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.