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Fuzzy basis functions, universal approximation, and orthogonal least-squares learning
1Dept. of Electr. Eng. and Comput. Sci., California Univ., Berkeley, CA.
IEEE Transactions on Neural Networks
|January 1, 1992
Summary
Fuzzy systems can approximate continuous functions using fuzzy basis functions. An orthogonal least-squares algorithm designs these systems, improving control performance for complex systems like the ball and beam.
Area of Science:
- Computational intelligence
- Control theory
- Fuzzy logic systems
Background:
- Fuzzy systems offer a powerful framework for modeling complex nonlinear systems.
- Approximation capabilities of fuzzy systems are crucial for their practical applications.
- Designing effective fuzzy systems often requires efficient learning algorithms.
Purpose of the Study:
- To demonstrate the approximation capabilities of fuzzy basis function expansions.
- To develop an orthogonal least-squares (OLS) learning algorithm for fuzzy system design.
- To evaluate the performance of the OLS-designed fuzzy system in a control application.
Main Methods:
- Utilizing the Stone-Weierstrass theorem to prove uniform approximation by fuzzy basis functions.
- Developing an OLS learning algorithm to select significant fuzzy basis functions from input-output data.
- Applying the fuzzy basis function expansion to approximate a controller for the nonlinear ball and beam system.
Main Results:
- The study proves that fuzzy basis function expansions can uniformly approximate any continuous function on a compact set.
- The OLS algorithm effectively designs fuzzy systems by selecting significant fuzzy basis functions.
- Simulation results indicate improved control performance for the ball and beam system using the proposed fuzzy controller.
Conclusions:
- Fuzzy basis function expansions provide a robust theoretical foundation for fuzzy system design.
- The OLS learning algorithm offers an efficient method for constructing accurate and parsimonious fuzzy systems.
- Incorporating common-sense fuzzy control rules enhances the performance of fuzzy controllers in practical applications.
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