Title: Multiple models reduction approach using gap metric for control of uncertain systems

Authors: Ali Zribi; Mohamed Chtourou; Mohamed Djemel

Addresses: Department of Electrical Engineering, National Engineering School of Sfax, B.P. 1173, 3038 Sfax, Tunisia. ' Department of Electrical Engineering, National Engineering School of Sfax, B.P. 1173, 3038 Sfax, Tunisia. ' Department of Electrical Engineering, National Engineering School of Sfax, B.P. 1173, 3038 Sfax, Tunisia

Abstract: In this paper, an internal multiple model control (IMMC) based on linear model's library is introduced. This approach supposes the definition of a set of local linear models. However, it remains beset with several difficulties such as the determination of the local models base. A new approach that combines fuzzy c-means (FCM) clustering algorithm and gap metric able to find the optimal number of local models is presented. The fuzzy clustering is used to divide the dataset into a large number of clusters where a local linear model is associated for each cluster. Then the gap metric analysis is applied to analyse the relationships among candidate local models, resulting in a reduced local models set. Such decomposition is shown to result in a set of stable and parsimonious models which can be deployed for online control.

Keywords: internal multiple model control; IMMC; fuzzy c-means; FCM; gap metric; linear model bank determination; model reduction; reduced order modelling; clustering algorithms; fuzzy clustering.

DOI: 10.1504/IJMIC.2012.048919

International Journal of Modelling, Identification and Control, 2012 Vol.17 No.2, pp.124 - 132

Published online: 17 Dec 2014 *

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