共查询到19条相似文献,搜索用时 156 毫秒
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基于T-S模糊模型的辨识算法 总被引:10,自引:0,他引:10
提出一种新的基于T-S模糊模型的辨识算法。该算法可分为2步,第1步是比较粗糙的辨识,按子空间的线性程度来划分输入空间,规则前件参数由于空间的中心和大小决定,规则后件线性参数由最小二乘法确定2步是模的精细调整,利用梯度下降法调节隶属函数和规则后件的线性参数,仿真实验说明了该算法的有效性。 相似文献
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首先, 引入后件直联型分层方法及其推理规则, 以对广义混合模糊系统的输入变量实施分层, 获得分层广义混合模糊系统的输入输出表达式和推理规则数的计算公式; 然后, 基于??- 积分模(度量) 和分片线性函数证明分层后广义混合模糊系统对一类可积函数具有逼近性; 最后, 通过模拟实例给出后件直联型分层广义混合模糊系统对可积函数的逼近过程. 模拟结果表明, 所提出的方法不仅能使原系统模糊规则总数大大减少, 而且能使分层后系统仍具有逼近性.
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在传统T-S模型的基础上,提出一种扩展T-S模型。该模型由一组模糊规则组成,由规则前件实现输入空间的划分,将成员函数及其函数变换引入规则后件以实现对输入子空间的非线性映射。对于该模型的建立,使用改进量子遗传算法优化规则前件,递推最小二乘法确定规则后件参数。通过对两个典型非线性系统辨识,仿真结果表明了该模型可以显著提高辨识精度,且具有很好的泛化性能。 相似文献
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本文在Type-1 T-S间接自适应模糊控制器的基础上,利用Type-2模糊系统理论,提出了区间Type-2 T-S间接自适应模糊控制器的设计方法.由于该系统的规则前件是区间Type-2模糊集合,后件为精确数,使构造的控制方法既具备Type-2模糊集处理诸多不确定性的特点,能够减少由于规则不确定对系统的影响,同时又具有T-S模糊模型后件为各输入变量的线性组合的特点,可以提高系统的建模精度,减少系统的规则数等优点.本文利用Lyapunov合成方法,研究了在所有变量一致有界的意义下,闭环系统的全局稳定性,分析了区间Type-2 T-S间接自适应模糊控制系统的收敛性,并给出了系统参数的自适应律.通过倒立摆跟踪模型进行仿真,验证其有效性和优越性. 相似文献
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利用模糊穴位映射理论,提出一种有效描述复杂多变量系统的模糊模型--广义模糊基函数展开式,它可方便地处理多输入多输出系统的语言和系统信息,并可逼近任意非线性函数,是一种通用的多变量模糊逻辑系统模型。利用语言信息,提出一种新的自适应参数辨识方法--改进的Widrow-Hoff学习规则,仿真结果验证了它的有效性。 相似文献
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基于模糊划分和支持向量机的TSK模糊系统 总被引:2,自引:0,他引:2
为了提高模糊系统处理高维问题的推广能力与鲁棒性能,提出将模糊聚类和支持向量机算法结合起来构造TSK模糊系统的算法.首先运用模糊聚类算法对输入空间进行划分,确定模糊规则前件的隶属函数.然后用支持向量机算法确定模糊规则的后件参数.该支持向量机的核函数是由模糊规则前件的隶属函数构造的,并且是Mercer核.在3个数据集的实验结果表明,与TSK模糊系统的传统算法和支持向量机相比较,本文算法具有更好的推广能力和鲁棒性. 相似文献
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Ke Zeng Nai-Yao Zhang Wen-Li Xu 《Fuzzy Systems, IEEE Transactions on》2000,8(6):773-780
Universal approximation is the basis of theoretical research and practical applications of fuzzy systems. Studies on the universal approximation capability of fuzzy systems have achieved great progress in recent years. In this paper, linear Takagi-Sugeno (TS) fuzzy systems that use linear functions of input variables as rule consequent and their special case, named simplified fuzzy systems that use fuzzy singletons as rule consequent, are investigated. On condition that overlapped fuzzy sets are employed, new sufficient conditions for simplified fuzzy systems and linear TS fuzzy systems as universal approximators are given, respectively. Then, a comparative study on existing sufficient conditions is carried out with numeric examples 相似文献
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Hao Ying Yongsheng Ding Shaokuan Li Shihuang Shao 《IEEE transactions on systems, man, and cybernetics. Part A, Systems and humans : a publication of the IEEE Systems, Man, and Cybernetics Society》1999,29(5):508-514
Both Takagi-Sugeno (TS) and Mamdani fuzzy systems are known to be universal approximators. We investigate whether one type of fuzzy approximators is more economical than the other. The TS fuzzy systems are the typical two-input single-output TS fuzzy systems. We first establish necessary conditions on minimal system configuration of the TS fuzzy systems as function approximators. We show that the number of the input fuzzy sets and fuzzy rules needed by the TS fuzzy systems depend on the number and locations of the extrema of the function to be approximated. The resulting conditions reveal the strength of the TS fuzzy approximators. The drawback, though, is that a large number of fuzzy rules must be employed to approximate periodic or highly oscillatory functions. We then compare these necessary conditions with the ones that we established for the general Mamdani fuzzy systems in our previous papers. Results of the comparison unveil that the minimal system configurations of the TS and Mamdani fuzzy systems are comparable. Finally, we prove that the minimal configuration of the TS fuzzy systems can be reduced and becomes smaller than that of the Mamdani fuzzy systems if nontrapezoidal or nontriangular input fuzzy sets are used. We believe that all the results in present paper hold for the TS fuzzy systems with more than two input variables but the proof seems to be mathematically difficult. Our new findings are valuable in designing more compact fuzzy systems, especially fuzzy controllers and models which are two most popular and successful applications of the fuzzy approximators 相似文献
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Necessary conditions on minimal system configuration for general MISO Mamdani fuzzy systems as universal approximators 总被引:3,自引:0,他引:3
Yongsheng Ding Hao Ying Shihuang Shao 《IEEE transactions on systems, man, and cybernetics. Part B, Cybernetics》2000,30(6):857-864
Recent studies have shown that both Mamdani-type and Takagi-Sugeno-type fuzzy systems are universal approximators in that they can uniformly approximate continuous functions defined on compact domains with arbitrarily high approximation accuracy. In this paper, we investigate necessary conditions for general multiple-input single-output (MISO) Mamdani fuzzy systems as universal approximators with as minimal system configuration as possible. The general MISO fuzzy systems employ almost arbitrary continuous input fuzzy sets, arbitrary singleton output fuzzy sets, arbitrary fuzzy rules, product fuzzy logic AND, and the generalized defuzzifier containing the popular centroid defuzzifier as a special case. Our necessary conditions are developed under the practically sensible assumption that only a finite set of extrema of the multivariate continuous function to be approximated is available. We have first revealed a decomposition property of the general fuzzy systems: A r-input fuzzy system can always be decomposed to the sum of r simpler fuzzy systems where the first system has only one input variable, the second one two input variables, and the last one r input variables. Utilizing this property, we have derived some necessary conditions for the fuzzy systems to be universal approximators with minimal system configuration. The conditions expose the strength as well as limitation of the fuzzy approximation: (1) only a small number of fuzzy rules may be needed to uniformly approximate multivariate continuous functions that have a complicated formulation but a relatively small number of extrema; and (2) the number of fuzzy rules must be large in order to approximate highly oscillatory continuous functions. A numerical example is given to demonstrate our new results. 相似文献
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Hao Ying 《Fuzzy Systems, IEEE Transactions on》1998,6(4):582-587
Takagi-Sugeno (TS) fuzzy systems have been employed as fuzzy controllers and fuzzy models in successfully solving difficult control and modeling problems in practice. Virtually all the TS fuzzy systems use linear rule consequent. At present, there exist no results (qualitative or quantitative) to answer the fundamentally important question that is especially critical to TS fuzzy systems as fuzzy controllers and models, “Are TS fuzzy systems with linear rule consequent universal approximators?” If the answer is yes, then how can they be constructed to achieve prespecified approximation accuracy and what are the sufficient renditions on systems configuration? In this paper, we provide answers to these questions for a general class of single-input single-output (SISO) fuzzy systems that use any type of continuous input fuzzy sets, TS fuzzy rules with linear consequent and a generalized defuzzifier containing the widely used centroid defuzzifier as a special case. We first constructively prove that this general class of SISO TS fuzzy systems can uniformly approximate any polynomial arbitrarily well and then prove, by utilizing the Weierstrass approximation theorem, that the general TS fuzzy systems can uniformly approximate any continuous function with arbitrarily high precision. Furthermore, we have derived a formula as part of sufficient conditions for the fuzzy approximation that can compute the minimal upper bound on the number of input fuzzy sets and rules needed for any given continuous function and prespecified approximation error bound, An illustrative numerical example is provided 相似文献
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《Information Sciences》2005,169(3-4):279-303
An efficient tool to deal with the ‘rule explosion’ problem is the hierarchical system by which a fuzzy system can be decomposed into a number of hierarchically connected low-dimensional systems. In this paper a generalized hierarchical Tagaki–Sugeno (TS) system is built. It is shown that the input–output (I/O) relationship of this generalized hierarchical system can be represented as one of a standard TS fuzzy system. And the system approximation capability is analyzed by taking piecewise linear functions as a bridge. By constructive method it is proven that the hierarchical fuzzy systems (HFS’s) can be universal approximators. For the given approximation accuracy, an estimation formula about the number of the rules needed in the HFS is established. Finally some simulation examples confirm that the HFS’s with smaller size rule base can approximate the given functions with high accuracy. The results obtained here provide us with the theoretical basis for various applications of HFS’s. 相似文献
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Approximation theory of fuzzy systems-MIMO case 总被引:12,自引:0,他引:12
In this paper, the approximation properties of MIMO fuzzy systems generated by the product inference are discussed. We first give an analysis of fuzzy basic functions (FBF's) and present several properties of FBF's. Based on these properties of FBF's, we obtain several basic approximation properties of fuzzy systems: 1) basic approximation property which reveals the basic approximation mechanism of fuzzy systems; 2) uniform approximation bounds which give the uniform approximation bounds between the desired (control or decision) functions and fuzzy systems; 3) uniform convergent property which shows that fuzzy systems with defined approximation accuracy can always be obtained by dividing the input space into finer fuzzy regions; and 4) universal approximation property which shows that fuzzy systems are universal approximators and extends some previous results on this aspect. The similarity between fuzzy systems and mathematical approximation is discussed and an idea to improve approximation accuracy is suggested based on uniform approximation bounds 相似文献