290 Int. J. Modelling, Identification and Control, Vol. 12, No. 3, 2011 Copyright © 2011 Inderscience Enterprises Ltd. A robust adaptive fuzzy wavelet network based controller for a class of non-linear systems Ayman Al-khazraji*, Najib Essounbouli and Abdelaziz Hamzaoui Centre de Recherche en STIC, IUT de Troyes, 9 rue de Québec B.P. 396 – F-10026 Troyes cedex, France E-mail: ayman.hussain@univ-reims.fr E-mail: najib.essounbouli@univ-reims.fr E-mail: abdelaziz.hamzaoui@univ-reims.fr *Corresponding author Abstract: This paper deals with the synthesis of an adaptive fuzzy wavelet network (FWN) controller for an nth order multi input multi output (MIMO) non-linear system suffering from parameters uncertainties and subjected to external perturbation. The proposed approach allows combining the advantages of the fuzzy logic system and those of wavelet networks to approximate quickly the unknown system dynamics with neither a prior knowledge about such dynamics nor offline learning phase. The FWN is adjusted online using some adaptation laws deduced from the stability analysis which guarantees a non-singular control action. Furthermore, the robustness of the proposed method is improved such that the knowledge of the upper bounds of both the external disturbances and the approximation errors is not required. Moreover, a variable sliding mode control (VSMC) technique is proposed to reduce the starting energy, caused by the presence of approximations errors and external disturbances, without deteriorating the tracking performances. To ensure the robustness of the overall closed loop system, analytical demonstration using Lyapunov theorem is considered. Finally, a numerical example is presented to validate our approach and to show the fast convergence, good tracking and the robustness of the closed loop system. Keywords: non-linear uncertain multi input multi output system; robust adaptive control; fuzzy wavelet system; sliding mode control. Reference to this paper should be made as follows: Al-khazraji, A., Essounbouli, N. and Hamzaoui, A. (2011) ‘A robust adaptive fuzzy wavelet network based controller for a class of non-linear systems’, Int. J. Modelling, Identification and Control, Vol. 12, No. 3, pp.290–303. Biographical notes: Ayman Al-khazraji received his BSc in Computer Engineering and MSc in Mechatronics both from the University of Technology, Baghdad, Iraq in 1998 and 2000 respectively. In 2008, he received his PhD in Control Engineering from Reims University, France. He spent more than five years with the computer engineering and information technology department, University of Technology, Baghdad, Iraq. Since 2005, he is working with Research Centre on STIC at Reims University, France to design different robust controllers for non-linear systems using the artificial intelligence. He published many papers in artificial intelligent based controller for non-linear system. His research interests include robust adaptive systems, fuzzy control theory, artificial intelligence applications in control, robotics and non-linear control system. Najib Essounbouli received his Maitrise from the University of Sciences and Technology of Marrakech (FSTG) in Morocco, his DEA in 2000, and his PhD in 2004 from Reims University of Champagne-Ardenne, all in Control Engineering. Since September 2005, he has been an Assistant Professor with IUT of Troyes, Reims University. He works on the areas of fuzzy logic control and robust adaptive control. Abdelaziz Hamzaoui received his degree in Electrical Engineering from the Polytechnic School of Algiers (ENPA), Algeria, in 1982; and his DEA (1989) and PhD (1992) from Reims University of Champagne-Ardenne, both in Electrical Engineering. He is a currently a Professor and Director of Technical Institute of Troyes, Reims University. He works on intelligent control, fuzzy control, robust adaptive control and power converters.