Title: Design of a sliding mode fuzzy observer for uncertain Takagi-Sugeno fuzzy model: application to automatic steering of vehicles

Authors: A. Akhenak, M. Chadli, J. Ragot, D. Maquin

Addresses: Centre de Recherche en Automatique de Nancy, UMR 7039, Nancy-Universite, CNRS 2, Avenue de la foret de Haye 54516, Vandœuvre-les-Nancy Cedex, France. ' Centre de Robotique, d'Electrotechnique et d'Automatique, Universite de Picardie, Jules Verne, 7, rue du Moulin Neuf, 80000, Amiens, France. ' Centre de Recherche en Automatique de Nancy, UMR 7039 Nancy-Universite, CNRS 2, Avenue de la foret de Haye 54516, Vandoeuvre-les-Nancy Cedex, France. ' Centre de Recherche en Automatique de Nancy, UMR 7039 Nancy-Universite, CNRS 2, Avenue de la foret de Haye 54516, Vandoeuvre-les-Nancy Cedex, France

Abstract: This paper addresses the analysis and design of a Sliding Mode Fuzzy Observer (SMFO) on the basis of a Takagi-Sugeno (T-S) fuzzy model. The main contribution of the paper is the development of a robust fuzzy observer with respect to the uncertainties as well as the synthesis of sufficient stability conditions of this observer. The stabilisation of the fuzzy observer is performed by the search of suitable Lyapunov matrices. It is shown how to determine the gains of the local observers, these gains being solutions of a set of Linear Matrix Inequalities (LMIs). The validity of the proposed methodology is illustrated by an estimation of the yaw rate of automatic steering of vehicles.

Keywords: Takagi-Sugeno fuzzy model; model uncertainty; fuzzy observers; sliding mode control; Lyapunov stability; linear matrix inequalities; LMI; yaw rate; automatic steering; vehicle steering.

DOI: 10.1504/IJVAS.2007.016405

International Journal of Vehicle Autonomous Systems, 2007 Vol.5 No.3/4, pp.288 - 305

Available online: 28 Dec 2007 *

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