International Journal of Intelligent Systems and Applications(IJISA)

ISSN: 2074-904X (Print), ISSN: 2074-9058 (Online)

Published By: MECS Press

IJISA Vol.4, No.11, Oct. 2012

Dynamic Recurrent Wavelet Neural Network Observer Based Tracking Control for a Class of Uncertain Nonaffine Systems

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A. Kulkarni, A. Kumar

Index Terms

Nonaffine Systems;Dynamic Recurrent Wavelet Networks;Nonlinear Observer;Lyapunov Stability Analysis


In this paper, a dynamic recurrent wavelet neural network observer and tracking control strategy is presented for a class of uncertain, nonaffine systems. In proposed scheme a dynamic recurrent wavelet network is used to design a nonlinear observer .Adaptation laws are developed for the online tuning of wavelet parameters. Based on the estimated states, a state feedback control law is derived to achieve the desired tracking performance. The stability of closed loop system and ultimate upper boundedness all closed loop signals is proven in Lyapunov sense. Effectiveness of proposed scheme is demonstrated through numerical simulation.

Cite This Paper

A. Kulkarni, A. Kumar,"Dynamic Recurrent Wavelet Neural Network Observer Based Tracking Control for a Class of Uncertain Nonaffine Systems", International Journal of Intelligent Systems and Applications(IJISA), vol.4, no.11, pp.53-61, 2012. DOI: 10.5815/ijisa.2012.11.06


[1]K.S. Narendra and K. Parthasarathy, “Identification and Control of Dynamical Systems Using Neural Networks” , IEEE Transactions on Neural Networks, Vol. 1, pp.4-27, March 1990.

[2]Qinghua Zhang and Albert Benveniste, “Wavelet Networks,” EEE Transactions On Neural Networks, Vol. 3, no. 6, pp.889-898, November 1992.

[3]Jun Zhang, Gilbert G. Walter, Yubo Miao, and Wan Ngai Wayne Lee, “Wavelet Neural Networks for Function Learning”, IEEE Transactions on Signal Processing, Vol. 43, no. 6, pp.1485-1497, June 1995. 

[4]B.Delyon, A. Juditsky, and A. Benveniste, “Accuracy Analysis for Wavelet Approximations”,IEEE Transactions on Neural Networks, Vol. 6, no. 2, pp.332-348 March 1995.

[5]Marios M. Polycarpou, Mark J. Mears and Scott E.Weaver, “Adaptive Wavelet Control of Nonlinear Systems”, Proceedings of the 36th Conference on Decision & Control, San Diego, California USA,pp.3890-3895, December 1997.

[6]Celso de Sousa, Jr., Elder Moreira Hemerly, and Roberto Kawakami Harrop Galvão, “Adaptive Control for Mobile Robot Using Wavelet Networks”,IEEE Transactions on Systems, Man, and Cybernetics—part B: Cybernetics, Vol. 32, pp.589-600, no. 4, August 2002.

[7]S. J. Yoo, J.B. Park and Y.H. Choi, “Self predictive control of chaotic systems using self recurrent wavelet neural network”, International journal of control, automation and systems, vol. 3 , no. 1, pp 43-55, March 2005.

[8]S. J. Yoo, J.B. Park and Y.H. Choi, “Direct adaptive control using self recurrent wavelet neural networks via adaptive learning rates for stable path tracking of mobile robots”, Proceedings of the 2005 American Control Conference, Portland, OR, USA, pp. 288-293, June 2005.

[9]S. Zenieh and A.L. Elshafei, “Robust control of uncertain nonlinear mechanical systems using a high gain observer”, Proceedings of American Control Conference, Chicago, IL USA, pp. 3620-3625, June 2000.

[10]K.C. Veluvolu and D. Lee, “Sliding mode high-gain observers for a class of uncertain nonlinear systems”, Applied Mathematics Letters, Vol. 24, pp. 1-6, March 2011.

[11]Li. Xiaoou and Yu. Wen, “Neural identification based on sliding mode observer”, 16th IEEE International Conference on Control Applications, Singapore, pp. 1-6, October 2007.

[12]A. N. Lakhal, A. S. Tlili, and N. Benhadj Braiek, “Neural Network Observer for Nonlinear Systems Application to Induction Motors ”, International Journal of Control and Automation Vol. 3, No. 1, pp. 1-16 March, 2010.

[13]Li. Xiaoou and Yu. Wen, “Nonlinear Observer Design Using Dynamic Recurrent Neural Networks”, Proceedings of the 35th Conference on Decision and Control, Japan pp. 949-954, December1996.

[14]B. Yang and A. Calise, “Adaptive control of a class of non affine systems using neural networks”, Proceedings of the 44th IEEE conference on decision and control and the European control conference, Spain, pp 2568-2573, Dec. 2005.

[15]J.K. Park, H.S. Huh and S.H. Kim, “Direct adaptive controller for non affine nonlinear systems using self structuring neural networks”, IEEE Transaction on neural networks, vol 16, no. 2, pp. 414-4212, 2005.

[16]K. J. Astrom and B. Wittenmark, Adaptive Control. New York: Addison Wesley, 1995.

[17]H.K. Khalil, Nonlinear Systems. Upper Saddle River, NJ: Printice Hall, 2002.