Adaptive control of nonlinear systems using fuzzy systems

Tayel Dabbous

doi:10.3934/jimo.2010.6.861

Article Contents

2010, Volume 6, Issue 4: 861-880. Doi: 10.3934/jimo.2010.6.861

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Adaptive control of nonlinear systems using fuzzy systems

Tayel Dabbous^1,

1.
Dep. of Elec. Eng., Higher Technological Institute, Ramadan 10th City

Received: February 28, 2007

Revised: May 31, 2010

Published: September 2010

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Abstract

In this paper we consider the adaptive control problem for a class of systems governed by nonlinear differential equations. Using Takagi-Sugeno approach, we have proposed a fuzzy model, which is linear in nature, the behavior of which is close to that of the unknown (nonlinear) plant. Based on this fuzzy model, we have proposed certain control structure with the help of which the plant output is capable of tracking certain desired trajectory. Using a suitable objective function and variation arguments, we have developed a set of necessary conditions with the help of which the parameters of the proposed fuzzy model and controller can be determined. Based on these necessary conditions, a numerical scheme is presented for computing the unknowns. Further, the question of continuous dependence of the proposed estimator and controller on system parameters (robustness) has been studied. Finally, the proposed adaptive control scheme has been applied to two different examples to illustrate the effectiveness of the proposed adaptive control scheme.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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