Robust adaptive fuzzy VSS control for a class of uncertain nonlinear systems using small gain design

Abstract

In this paper, a novel robust adaptive fuzzy variable structure control (RAFVSC) scheme is proposed for a class of uncertain nonlinear systems. The uncertain nonlinear system and gain functions originating from modeling errors and external disturbances are all unstructured (or non-repeatable), state-dependent and completely unknown. The Takagi–Sugeno type fuzzy logic systems are used to approximate uncertain functions in the systems and the RAFVSC is designed by use of the input-to-state stability (ISS) approach and small gain theorem. In the algorithm, there are three advantages which are that the asymptotic stability of adaptive control in the presence of unstructured uncertainties can be guaranteed, the possible controller singularity problem in some of existing adaptive control schemes using feedback linearization techniques can be removed and the adaptive mechanism with minimal learning parameterizations can be achieved. The performance and effectiveness of the proposed methods are discussed and illustrated with two simulation examples.

Keywords:

• Adaptive tracking control
• Fuzzy logic control
• Variable structure system (VSS)
• Uncertain nonlinear systems
• Small gain theorem

Acknowledgements

This work was supported in part by the Research Fund for the Doctoral Program of Higher Education under Grant No. 20020151005, the Science Foundation under Grant No. 95-06-02-22 and the Young Investigator Foundation under Grant No. 95-05-05-31 of the national ministry of communications of P. R. China.