Optimal adaptive fuzzy control for a class of unknown nonlinear systems

  • Authors:

  • I. Lagrat;A. El Ougli;I. Boumhidi

  • Affiliations:

  • Département de Physique, Université Sidi Mohamed Ben Abdellah, LESSI, Faculté Des Sciences Dhar el Mehraz, Fés Morocco;Département de Physique, Université Sidi Mohamed Ben Abdellah, LESSI, Faculté Des Sciences Dhar el Mehraz, Fé Morocco;Département de Physique, Université Sidi Mohamed Ben Abdellah, LESSI, Faculté Des Sciences Dhar el Mehraz, Fés Morocco

  • Venue:
  • WSEAS Transactions on Systems and Control
  • Year:
  • 2008

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Abstract

In this paper, we present an optimal adaptive fuzzy controller for a class of nonlinear systems with unknown nonlinear dynamics. The strategy of control is based on the fuzzy systems and linear matrix inequalities (LMI). The adaptive fuzzy logic system is used to approximate the unknown dynamics; we exploit the linear structure of a Takagi-Sugeno fuzzy system with constant conclusion to design an indirect adaptive fuzzy controller. The auxiliary compensation control is added to attenuate the influence of external disturbances and to remove fuzzy approximation error. The design of the auxiliary control relies on LMI and the Lyapunov technique for achieving stability and specified performance. The adaptation laws of the adjustable parameters are deduced from the stability analysis, in the sense of Lyapunov, to get a more accurate approximation level. Simulation results are given to illustrate the tracking performance.