SISO Mamdani模糊系统作为函数逼近器的必要条件  

Preconditions for SISO Mamdani fuzzy systems to perform as function approximators

作　　者：孙富春[1] 杨晋[1] 刘华平[1] 

机构地区：[1]清华大学智能技术与系统国家重点实验室,北京100084

出　　处：《智能系统学报》2009年第4期288-294,共7页CAAI Transactions on Intelligent Systems

基　　金：国家自然科学杰出青年基金资助项目(60625304);国家自然科学基金资助项目(90716021;60621062)

摘　　要：模糊系统已被证明是通用逼近器,但实现高精度通常需要大量规则.模糊系统满足给定精度的必要条件能指导最优系统的构造,如输入输出模糊集、模糊规则的选取.研究了单输入单输出(SISO)Mamdani模糊系统在给定逼近精度下作为函数逼近器的必要条件.由于通用型SISO Mamdani模糊系统在划分子区间单调,所以模糊系统的最优配置是输入域的划分数至少为系统输出的单调性变化次数.当模糊系统满足给定逼近精度时,通过分析目标函数的局部特性,基于目标函数的极点,建立了SISO Mamdani模糊系统的必要条件.更重要的是证明了现有的必要条件仅仅是该文结论的一种特例.最后,使用数值实例来验证该文的结论,分析模糊系统作为函数逼近器的优劣.It has been proven that fuzzy systems are universal approximators. However, a large number of rules are usually needed for high accuracy. Knowledge of conditions necessary for a fuzzy system to have a given level of accuracy can provide guidance for design of an optimal system, such as selection of optimal input/output fuzzy sets and fuzzy rules. The necessary conditions for a single-input single-output （SISO） Mamdani fuzzy system to operate as a function approximator subject to a given precision were discussed. Since the general SISO Mamdani fuzzy system is monotonic at subintmwals, its optimal configuration is when the number of division points is not less than the number of times its monotonicity changes. Thus by analyzing the local characteristics of the object function under the fuzzy system, necessary conditions for a SISO Mamdani fuzzy systems were obtained in accordance with the extrema of the object function. Furthermore, it was shown that the necessary conditions found in prior documents are only a special case of those described here. Finally, simulation examples were given to verify our conclusions and analyze the performance as well as the limitations of a fuzzy system as a function approximator.

关 键 词：模糊系统 必要条件 模糊规则 逼近精度 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]