齐次T-S模糊系统的逼近性能

为深入剖析模糊系统的通用逼近性能,明确定义了输入模糊集的有关概念和模糊系统输入空间的标准双交叠模糊划分,给出了在此定义下的模糊系统的一些基本性质.构造了一类输入变量采用伪梯形隶属函数的一般齐次T-S(CHTS)模糊系统,进而证明了此类T-S模糊系统能够以任意精度逼近满足Lipschitz条件的任意非线性函数,定理假设的保守性得以降低,结论更具一般性.仿真结果验证了齐次T-S模糊系统的通用逼近性,为基于平行分布补偿(PDC)原理和线性矩阵不等式(LMI)的T-S模糊控制系统的设计和稳定性分析提供了理论依据.

Approximation capabilities of homogeneous T-S fuzzy systems

To analyze the universal approximation capabilities of fuzzy systems,some definitions of input fuzzy sets were developed and the normal two-lapped fuzzy partition(NTLFP) in the input space of fuzzy systems was well defined.Some corresponding essential properties were presented.A class of common homogeneous T-S(CHTS) fuzzy systems was constructed using pseudo trapezoid shaped input membership functions,and it was proved to approximate any nonlinear functions satisfying Lipschitz condition to any degree of accuracy.The conclusion relaxes the conservative assumption of previous literatures,therefore,it is more universal.A simulation example demonstrates the effectiveness of CHTS fuzzy systems universal approximation.The results provide theoretical foundation for the systematic design and stability analysis of T-S fuzzy control systems based on parallel distributed compensation(PDC) principle and linear matrix inequality(LMI).