典型T-S模糊系统是通用逼近器

曾  珂; 张乃尧; 徐文立

引用本文:	曾珂,张乃尧,徐文立.典型T-S模糊系统是通用逼近器[J].控制理论与应用,2001,18(2):293~297.[点击复制]
	ZENG Ke,ZHANG Nai-yao,XU Wen-li.Typical T-S Fuzzy Systems Are Universal Approximators[J].Control Theory and Technology,2001,18(2):293~297.[点击复制]

典型T-S模糊系统是通用逼近器

Typical T-S Fuzzy Systems Are Universal Approximators

摘要点击 2181 全文点击 1556 投稿时间：1999-07-15 修订日期：2000-02-14

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DOI编号 10.7641/j.issn.1000-8152.2001.2.032

2001,18(2):293-297

中文关键词典型T-S模糊系统通用逼近性在线学习

英文关键词 typical T-S fuzzy systems universal approximation online learning

基金项目国家自然科学基金(69774015); 清华大学基础研究基金资助项目.

作者	单位
曾珂	清华大学自动化系, 北京 100084
张乃尧	清华大学自动化系, 北京 100084
徐文立	清华大学自动化系, 北京 100084

中文摘要

研究的多输入单输出T-S模糊系统采用输入变量的线性函数作为规则后件, 称为典型T-S模糊系统, 在每个输入变量的模糊子集满足一致性以及隶属函数连续且分段可微的条件下, 证明了典型T-S模糊系统是通用逼近器. 以此为基础, 提出当典型T-S模糊系统采用BP算法进行在线学习时, 可以仅调节规则后件的参数, 而同时仍然能够确保通用逼近性.

英文摘要

The multi input single output T-S fuzzy systems investigated in this paper, named as typical T-S fuzzy systems, use linear functions of input variables as rule consequents. On the condition that fuzzy sets of each input variable are consistent and all the membership functions are continuous and piecewise differentiable, we proved that typical T-S fuzzy systems are universal approximators. Based on the proof, we further pointed out that it's feasible to modify only the rule consequent parameters of typical T-S fuzzy systems when it carries out online learning, however the universal approximation capability is still ensured.