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Fuzzy local linearization and local basis function expansion in nonlinear system modeling.

Q Gan1, C J Harris

  • 1Dept. of Electron. & Comput. Sci., Southampton Univ.

IEEE Transactions on Systems, Man, and Cybernetics. Part B, Cybernetics : a Publication of the IEEE Systems, Man, and Cybernetics Society
|February 7, 2008
PubMed
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Fuzzy local linearization offers advantages over local basis function expansion for modeling nonlinear processes. This method uses Takagi-Sugeno fuzzy models and B-splines for efficient and parsimonious system representation.

Area of Science:

  • Engineering
  • Computer Science
  • Mathematics

Background:

  • Nonlinear systems present significant modeling challenges.
  • Existing methods like local basis function expansion have limitations.

Purpose of the Study:

  • To compare fuzzy local linearization with local basis function expansion for nonlinear process modeling.
  • To introduce a novel approach combining Takagi-Sugeno fuzzy models and B-splines.

Main Methods:

  • Fuzzy local linearization using first-order Takagi-Sugeno fuzzy models.
  • Analysis of Variance (ANOVA) decomposition for system analysis.
  • B-splines as membership functions for input space partitioning.
  • Modified Algorithm for Adaptive Spline Modeling of Observation Data (MASMOD) for parsimonious model development.

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Main Results:

  • Fuzzy local linearization models demonstrate superior performance compared to local basis function expansion.
  • The MASMOD algorithm effectively determines optimal B-spline configurations.
  • Achieved parsimonious models with high accuracy for nonlinear systems.

Conclusions:

  • Fuzzy local linearization is a highly effective technique for nonlinear system modeling.
  • The proposed method offers advantages in terms of model simplicity and accuracy.
  • This approach provides a robust framework for understanding and controlling complex nonlinear dynamics.