Document Type : Research Paper


1 Department of Electrical engineering, Faculty of Sciences and Technology, University Larbi Tebessi of Tebessa, 12000 Tebessa, Algeria

2 LAAAS Laboratory, Faculty of Technology, Department of Electronics, University of Batna 2, 5000 Batna , Algeria

3 Department of Electronics , Faculty of Sciences and Technology, University of Bordj Bou Arreridj, 34000 BBA, Algeria


The problem of disturbance rejection in the control of nonlinear systems with additive disturbance generated by some unforced nonlinear systems, was formulated and solved by {\itshape Mukhopadhyay} and {\itshape Narendra}, they applied the idea of increasing the order of the system, using neural networks the model of multilayer perceptron on several systems of varying complexity, so the objective of this work is using the same idea with two other recent methods fast and reliable ; fuzzy set systems and hybrid neuro-fuzzy systems respectively to compute the control law which minimizes the effect of the disturbance at the output of nonlinear systems. The application of the methods previously cited in form of results is presented to determine the identification model and to provide theoretical justification to existence a solution of disturbance rejection. Our better results with fuzzy systems and neuro-fuzzy systems are presented and discussed in detail in this paper with several systems of increasing complexity.


[1] A. Amini and N. Nikraz , Proposing two defuzzification methods based on output fuzzy set
weights ,I.J. Intelligent Systems and Applications, 8 (2016), 1–12.
[2] A. T. Azar, Adaptive neuro-fuzzy systems, Fuzzy Systems, INTECH, Croatia, (2010), 85–110.
[3] A. Ajoudani and A. Erfanian ,A neuro-sliding-mode control with adaptive modeling of uncertainty
for control of movement in paralyzed limbs using functional electrical stimulation,
IEEE Trans On Biomedical Engineering, 56 (2009), 1771–1780.
[4] D. Bajpai and A. Mandal, Comparative analysis of T-sugeno and mamdani type fuzzy logic
controller for PMSM drives, International Journal of Engineering Research and General
Science , 3 (2015), 495–507.
[5] R. Fuller ,Introduction to neuro-fuzzy systems , Advances in Soft Computing Series, Springer-
Verlag, Berlin Heildelberg, 2 (2000), 1–289.
[6] S. Ledesma, G. Cerda, G. AvĖ‡ina, D. Hernandez and M. Torres,Feature selection using artificial
neural networks, Springer-Verlag Berlin Heidelberg, 5317 (2008), 351–359.
[7] K. Mondal, P. Dutta and S. Bhattacharyya ,Efficient fuzzy rule base design using image
features for image extraction and segmentation, Fourth International Conference on Computational
Intelligence and Communication Networks, (2012), 793–799.
[8] M. Mizumoto, Products-sum-gravity method fuzzy singleton-type reasoning method simplified
fuzzy reasoning method, IEEE International Conference on Fuzzy Systems, 3 (1996), 2098-
[9] S. Mukhopadhyay and K. S. Narendra, Disturbance rejection in nonlinear systems using
neural networks, IEEE Transactions on Neural Networks, 4 (1993), 63–72.
[10] K. S. Narendra and K. Parthasarathy, Identification and control of dynamical systems using
neural networks, IEEE Trans on Neural Networks, 1 (1990), 4–27.
[11] A. K. Palit and G. Doeding ,Backpropagation based training algorithm for Takagi-Sugeno
type mimo neuro-fuzzy network to forecast electrical load time series, IEEE International
Conference on Fuzzy Systems, (2002), 1-6.
[12] K. Parthasarathy and K. S Narendra, Stable adaptive control of a class of discret-time nonlinear
systems using radial neural networks, Center for Systems Science, Yale University ,
CT, (1991), Technical Report No 9103.
[13] J. J. E. Slotine and W. Li, Applied nonlinear control, Englewood Cliffs, NJ: Prentice-Hall,
199 (1991), 1–478.
[14] J .Vieira, F .Morgado and A. Mota, Neuro-fuzzy systems: a survey, 5th WSEAS NNA
International Conference on Neural Networks and Applications, Udine, Italy, (2004), 1–6.
[15] K. Vishnu Lakshmi and M. Sathik Raja, Genetic algorithm based brain tumor detection
and segmentation , International Journal of Innovative Research in Advanced Engineering
(IJIRAE), 4 (2017), 40–47.
[16] D. Wu ,Fuzzy sets and systems in building closed-loop affective computing systems for
Human-computer interaction: advances and new research directions, IEEE International
Conference on Fuzzy Systems, (2012) , 1–8.
[17] L. X. Wang, A Course in Fuzzy Systems and Control, Prentice Hall, Upper Saddle River,
New Jersey, (1997), 1–222.
[18] L. X. Wang and J. M. Mendel, Back-propagation fuzzy system as nonlinear dynamic system
identifiers , IEEE International Conference on Fuzzy Systems, (1992), 1409-1418.