Advertisement

Adaptive T–S Fuzzy Control with Unknown Membership Functions

  • Ruiyun Qi
  • Gang Tao
  • Bin Jiang
Chapter
Part of the Communications and Control Engineering book series (CCE)

Abstract

In the previous chapter, the T–S fuzzy dynamic systems were formulated into linearly parametrized models, based on which parameter adaptive laws were designed and closed-loop system stability was analyzed. However, there are two group of parameters in a T–S fuzzy system: consequent parameters and membership functions parameters. The former are usually linearly dependent parameters while the latter are usually nonlinearly dependent, i.e., parameters of Gaussian or Sigmoidal membership functions. Most adaptive control approaches assume the parameters of membership functions are accurate enough so that only the uncertainties in consequent parameters are considered. However, in practice, it is difficult to set the membership function parameters accurately in advance. In this chapter, we address such an issue using an adaptive estimation method with a gradient algorithm derived based on a nonlinearly parameterized error model resulted from the parameter nonlinearity of membership functions.

References

  1. Goodwin GC, Sin KS (1984) Adaptive filtering prediction and control. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  2. Ioannou PA, Sun J (1996) Robust adaptive control. Prentice-Hall, Englewood CliffszbMATHGoogle Scholar
  3. Qi R, Tao G, Tan C (2011) An adaptive control scheme for discrete-time T–S fuzzy systems with unknown membership parameters. In: Proceedings of the 8th Asia control conference. Taiwan, pp 1164–1169Google Scholar
  4. Tanaka K, Ikeda T, Wang HO (1996) Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, \(H^{\infty }\) control theory, and linear matrix inequalities. IEEE Trans Fuzzy Syst 4:1–13CrossRefGoogle Scholar
  5. Tao G (2003) Adaptive control design and analysis. Wiley, New YorkCrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Ruiyun Qi
    • 1
  • Gang Tao
    • 2
  • Bin Jiang
    • 1
  1. 1.College of Automation EngineeringNanjing University of Aeronautics and AstronauticsNanjingChina
  2. 2.School of Engineering and Applied ScienceUniversity of VirginiaCharlottesvilleUSA

Personalised recommendations