Fuzzy basis functions, universal approximation, and orthogonal least-squares learning

  • Authors:
  • L. -X. Wang;J. M. Mendel

  • Affiliations:
  • Dept. of Electr. Eng. & Comput. Sci., California Univ., Berkeley, CA;-

  • Venue:
  • IEEE Transactions on Neural Networks
  • Year:
  • 1992

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Abstract

Fuzzy systems are represented as series expansions of fuzzy basis functions which are algebraic superpositions of fuzzy membership functions. Using the Stone-Weierstrass theorem, it is proved that linear combinations of the fuzzy basis functions are capable of uniformly approximating any real continuous function on a compact set to arbitrary accuracy. Based on the fuzzy basis function representations, an orthogonal least-squares (OLS) learning algorithm is developed for designing fuzzy systems based on given input-output pairs; then, the OLS algorithm is used to select significant fuzzy basis functions which are used to construct the final fuzzy system. The fuzzy basis function expansion is used to approximate a controller for the nonlinear ball and beam system, and the simulation results show that the control performance is improved by incorporating some common-sense fuzzy control rules