Wang L X, Mendel J M
Dept. of Electr. Eng. and Comput. Sci., California Univ., Berkeley, CA.
IEEE Trans Neural Netw. 1992;3(5):807-14. doi: 10.1109/72.159070.
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.
模糊系统被表示为模糊基函数的级数展开，而模糊基函数是模糊隶属函数的代数叠加。利用斯通 - 魏尔斯特拉斯定理，证明了模糊基函数的线性组合能够以任意精度在紧集上一致逼近任何实连续函数。基于模糊基函数表示，开发了一种正交最小二乘（OLS）学习算法，用于根据给定的输入 - 输出对设计模糊系统；然后，使用OLS算法选择用于构建最终模糊系统的重要模糊基函数。模糊基函数展开用于逼近非线性球杆系统的控制器，仿真结果表明，通过纳入一些常识性模糊控制规则，控制性能得到了改善。
