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Non-linear processes, by their nature, are non-uniform and invariably require custom designed control schemes to deal with individual characteristics. No general theory deals comprehensively with the wide range of non-linear systems encountered. In an attempt to accurately model non-linear dynamical systems, a wide variety of techniques have been developed such as non-linear auto-regressive moving average with exogeneous inputs (NARMAX) models (Chen and Billings, 1989), Weiner models (Schetzen, 1981), Hammerstein models (Billings and Fakhouri, 1982) and Multiple Layer Perceptron (MLP) neural networks (Narendra and Kannan, 1990). While the accuracy of such models offers a potentially significant improvement over linear models, the process control engineer is faced with the difficulty in their more-or-less so-called black-box representation of dynamics of non-linear systems. This back-box representation fails to exploit the significant theoretical results available in the conventional modelling and control domain, making it difficult to analyse the behaviour of the controlled system and to prove its stability. The last decade has shown an increase in the use of local model representations of non-linear dynamic systems. The basic structure includes a number of approaches: Tagaki-Sugeno (1985) fuzzy systems, local model networks (Johansen and Foss 1993), gain-scheduled control (Shamma and Athans, 1990), the smooth threshold autoregressive (STAR) models of Tong (1990) and the state dependent models of Priestley (1988). The model parameters are obtained from prior knowledge, linearization of a physical model or identified from measured data. The advantages of these approaches are purported to be their simplicity and the insight into global dynamics obtained from their local models. The construction of interpolating the behaviour of locally valid models offers an attractive and intuitively pleasing method of modelling non-linear systems. Moreover, in terms of control, it potentially provides a convenient framework for obtaining both stability and improved performance simultaneously. Despite the wide applications of multiple model networks in non-linear systems and the growing interest in this area, there is a notable lack of a formal review of the literature. This paper intends to provide a systematic presentation of features, advantages and problems encountered in the application of multiple model networks application in modelling for control. The scope of this paper includes the main theoretical results and brief design procedures relating to multiple model networks with the aim of providing both a critical overview and a useful entry point into the relevant literature. Furthermore, it explores the links between the fields of control science and multiple model networks in a unified presentation and identifies the key areas for future research.
Gao, Ruiyao and O'Dwyer, Aidan : Multiple model networks in non-linear system modelling for control – a review. Proceedings of the 3nd Wismarer Automatisierungssymposium, Wismar, Germany, September, Paper 1.3-3.