首先针对双输入单输出模糊系统提出了一种模糊变换方法,指出这种模糊变换不仅与单输入和单输出模糊系统有密切的联系,而且利用这种模糊变换构造的模糊系统具有很好的泛逼近性.然后将这种模糊变换应用到模糊推理建模法中,导出了所研究的模糊系统的微分方程模型和状态空间模型,从而给出了一种新的模糊推理建模法.理论分析和仿真实验均表明:利用模糊变换构造的微分方程对所研究的模糊系统具有很好的泛逼近性.
Abstract
In this paper,we puts forward a fuzzy transformation method for double-input-single-output fuzzy system,and points out that not only this fuzzy transformation has intimate connections with single-input-single-output fuzzy systems,but also the fuzzy system constructed with this fuzzy transformation has good universal approximation.By applying the fuzzy transformation to the fuzzy reasoning modeling method,we establish a new fuzzy reasoning modeling method and derive the differential equation model and the state-space model for the system which is studied.The theoretical analysis and simulate experiment show that the differential equations based on fuzzy transformation have good universal approximation.
关键词
模糊控制 /
模糊变换 /
泛逼近性 /
HX方程 /
状态空间模型
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Key words
fuzzy control /
fuzzy transformation /
universal approximation /
differential equations /
state space model
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中图分类号：
TP13
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参考文献
[1] 王立新著,王迎军译.模糊系统与模糊控制教程[M].北京:清华大学出版社,2003.1-99. Wang Lixin.A Course in Fuzzy Systems and Control[M].Beijing:Tsinghua U niversity Press,2003.1-99.(in Chinese)
[2] Yuan Xuehai,et al.The center-of-gravity fuzzy systems based on the normal fuzz y implications[J].Computer and Mathematics with Applications,2011,61(9):2879-2 898.
[3] Li Y M,Shi Z K,Li Z H.Approximation theory of fuzzy systems based upon genuine m any-valued implication-SISO case[J].Fuzzy Sets and Systems,2002,130(2):147-1 57.
[4] X J Zeng,M G Singh.Approximation theory of fuzzy systems-SISO case[J].IEEE Tr ansactions on Fuzzy Systems,1994,2(2):162-176.
[5] 王加银,刘民,李洪兴.单入单出模糊控制器函数与插值式的偏差分析[J].电子学报,2009,3 7(2):424-428. Wang Jia-yin,Liu Min,Li Hong-xing.Analysis of difference between control funct ion and interpolation expression of SISO fuzzy controller[J].Acta Electronica Sinica,2009,37(2):424-428.(in Chinese)
[6] 单伟伟,等.变论域自适应模糊控制器的CMOS模拟电路芯片实现[J].电子学报,2009,37(5): 913-917. Shan Wei-wei,et al.Variable universe adaptive fuzzy logic controller CMOS analo g chip implementation[J].Acta Electronica Sinica,2009,37(5):913-917.(in Chines e)
[7] 袁学海,等.基于参数单点模糊化方法的模糊系统及其逼近能力[J].电子学报,2011,39(10) :2372-2377.[JP] Yuan Xue-hai,et al.Fuzzy systems and their approximation capability based on pa rameter singleton fuzzifier methods[J].Acta Electronica Sinica,2011,39(10):237 2-2377.(in Chinese)
[8] Zadeh L A.The concept of a linguistic variable and its application to approximat e reasoning I[J].Information Sciences,1975,8(3):199-251.
[9] 王国俊.非经典逻辑与近似推理[M].北京:科学出版社,2000.1-91. Wang Guojun.Non-Classical Logic and Approximate Reasoning[M].Beijing:Science Press,2000.1-91.(in Chinese)
[10] Li Hongxing.Interpolation mechanism of fuzzy control[J].Science in China(Serie s E),1998,41(3):312-320.
[11] Li Hongxing,et al.Modeling on fuzzy control systems[J].Science in China (Serie s A),2002,45(12):1506-1517.
[12] 李洪兴,宋文彦,等.基于Fuzzy推理的时变系统建模[J].系统科学与数学,2009,29(8):1109 -1128. Li Hongxing,Song Wenyan,et al.Time-varying system modeling method based on fuzz y inference[J].Journal of Systems Science and Complexity,2009,29(8):1109-1128. (in Chinese)
[13] Yang Xue,Wang Xiaotian,et al.Center of gravity fuzzy systems and the probability distributions based on the circle operators[A].International Conference on Co mputer Design and Applications(ICCDA)[C].USA:IEEE,2011.402-406.
[14] 袁学海,李洪兴.基于输入-输出数据的概率分布及其数字特征[J].模糊系统与数学,2011,2 5(1):69-78. Yuan Xuehai,Li Hongxing.The probability distributions and numerical characterist ics based on a set data of input-output[J].Fuzzy Systems and Mathematics,2011 ,25(1):69-78.(in Chinese)
[15] H Ying.Sufficient conditions on general fuzzy systems as function approximators [J].Automatica,1994,30(3):521-525.
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脚注
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基金
国家自然科学基金 (No.90818025,No.61074044)
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