Adaptive T–S Fuzzy Control with Unknown Membership Functions
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.
- 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