Feedback Linearization with Fuzzy Compensation for Uncertain Nonlinear Systems

Marcelo Costa Tanaka, Josiane Maria de Macedo Fernandes, Wallace Moreira Bessa


This paper presents a nonlinear controller for uncertain single-input-single-output (SISO) nonlinear systems. The adopted approach is based on the feedback linearization strategy and enhanced by a fuzzy inference algorithm to cope with modeling inaccuracies and external disturbances that can arise. The boundedness and convergence properties of the tracking error vector are analytically proven. An application of the proposed control scheme to a second-order nonlinear system is also presented. The obtained numerical results demonstrate the improved control system performance.


Feedback linearization; Fuzzy logic; Nonlinear control; Van der Pol oscillator

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R. Boukezzoula, S. Galichet, and L. Foulloy. Fuzzy feedback linearizing controller and its equivalence with the fuzzy nonlinear internal model control structure. International Journal of Applied Mathematics and Computer Science, 17(2):233–248, 2007.

F.-C. Chen. Back-propagation neural networks for nonlinear self-tuning adaptive control. IEEE Control Systems Magazine, 10(3):44–48, 1990.

M. S. Couceiro, N. M. F. Ferreira, and J. A. T. Machado. Hybrid adaptive control of a dragonfly model. Communications in Nonlinear Science and Numerical Simulation, 17:893–903, 2012.

H. Deng, H.-X. Li, and Y.-H. Wu. Feedback-linearization-based neural adaptive control for unknown nonaffine nonlinear discrete-time systems. IEEE Transactions on Neural Networks, 19(9):1615–1625, 2008.

M. Hojati and S. Gazor. Hybrid adaptive fuzzy identification and control of nonlinear systems. IEEE Transactions on Fuzzy Systems, 10(2):198–210, 2002.

H.-J. Kang, C. Kwon, H. Lee, and M. Park. Robust stability analysis and design method for the fuzzy feedback linearization regulator. IEEE Transactions on Fuzzy Systems, 6(4):464–472, 1998.

B. Kosko. Fuzzy systems as universal approximators. IEEE Transactions on Computers, 43(11):1329–1333, 1994.

F. L. Lewis, W. K. Tim, L.-Z. Wang, and Z. X. Li. Deadzone compensation in motion control systems using adaptive fuzzy logic control. IEEE Transactions on Control Systems Technology, 7(6):731–742, 1999.

Z. Lu, L.-S. Shieh, G. Chen, and N. P. Coleman. Adaptive feedback linearization control of chaotic systems via recurrent high-order neural networks. Information Sciences, 176:2337–2354, 2006.

J. O. Pedro and O. A. Dahunsi. Neural network based feedback linearization control of a servo-hydraulic vehicle suspension system. International Journal of Applied Mathematics and Computer Science, 21(1):137–147, 2011.

J.-J. E. Slotine and W. Li. Applied Nonlinear Control. Prentice Hall, New Jersey, 1991.

X.-S. Wang, C.-Y. Su, and H. Hong. Robust adaptive control of a class of nonlinear systems with unknow dead-zone. Automatica, 40:407–413, 2004.

A. Yesildirek and F. L. Lewis. Feedback linearization using neural networks. Automatica, 31(11):1659–1664, 1995.


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