一般齐次T-S模糊系统的逼近性能  

Study on approximation capabilities of general homogenous T-S fuzzy systems

作　　者：王宁[1] 谭跃[1] 王丹[1] 吴志良[1] 

机构地区：[1]大连海事大学轮机工程学院,辽宁大连116026

出　　处：《智能系统学报》2010年第5期436-442,共7页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学基金资助项目(51009017);中央高校基本科研业务费专项资金资助项目(2009QN025)

摘　　要：为剖析一般齐次T-S模糊系统的逼近性能,通过广泛总结常用模糊集的特点,明确定义了一种具有普遍意义的输入空间的一般模糊划分(GFP).基于输入采用GFP的一般齐次T-S模糊系统的解析结构,证明了该类一般齐次T-S模糊系统能够以任意精度逼近任意非线性函数,并得到了一个其作为通用逼近器的充分条件.作为GFP的一种退化,进一步研究了输入采用线性模糊划分(LFP)的一般齐次T-S模糊系统的一阶逼近性能.仿真实例验证了所得理论结果的有效性,并考察了充分条件的保守性.这为基于齐次T-S模糊模型的复杂系统建模与控制提供了理论指导.In order to analyze approximation capabilities of general homogenous T-S fuzzy systems, the general fuzzy partition （GFP） with universal significance was definitely defined in the input space of fuzzy systems through comprehensively summarizing properties of common fuzzy sets. Based on the analytical structure, a large class of general homogenous T-S fuzzy systems was proven to be able to approximate any nonlinear function to any degree of accuracy, and a sufficient condition for the introduced fuzzy systems to be the universal approximator was proposed. Concerning the degeneration of the GFP, the linear fuzzy partition （LFP） in the input space of fuzzy systems was also defined to further investigate first-order approximation capabilities of general homogenous T-S fuzzy systems. Simulation studies demonstrated that the presented theoretical results are effective and the sufficient condition was investigated to be conservative. These results provide a theoretical foundation for complex system modeling and control based on homogenous T-S fuzzy systems.

关 键 词：齐次T—S模糊系统 逼近性能 复杂系统 模糊划分 

分 类 号：O159[理学—数学]