Continuity of Defuzzification on L2 Space for Optimization of Fuzzy Control
Continuity of Defuzzification on L2 Space for Optimization of Fuzzy Control
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DOI：
10.1007/978-3-642-35236-2_8
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发表时间：
2012-12
期刊：
影响因子：
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通讯作者：
T. Mitsuishi;Takanori Terashima;Nami Shimada;Toshimichi Homma;K. Sawada;Y. Shidama
中科院分区：
文献类型：
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作者：
T. Mitsuishi;Takanori Terashima;Nami Shimada;Toshimichi Homma;K. Sawada;Y. Shidama
本研究的目的是考虑基于泛函分析的模糊最优控制。我们使用一种数学方法来计算最优解。模糊控制的反馈通过近似推理，采用和中心去模糊化方法或IF-THEN模糊规则的高度法进行估计。该框架由两个命题组成：为了保证最优解的收敛，从连续函数空间中选取的一组模糊隶属度函数(允许模糊控制器)是紧度量的。并假设近似推理是隶属函数集上的泛函，证明了它的连续性。然后，证明了使非线性反馈模糊系统的积分性能函数最小化(最大化)的模糊控制器的存在性。
The purpose of this study is to consider the fuzzy optimal control based on the functional analysis. We used a mathematical approach to compute optimal solutions. The feedback of fuzzy control is evaluated through approximate reasoning using the center of sums defuzzification method or the height method on IF-THEN fuzzy rules. The framework consists of two propositions: To guarantee the convergence of optimal solution, a set of fuzzy membership functions (admissible fuzzy controller) which are selected out of continuous function space is compact metrizable. And assuming approximate reasoning to be a functional on the set of membership functions, its continuity is proved. Then, we show the existence of a fuzzy controller which minimizes (maximizes) the integral performance function of the nonlinear feedback fuzzy system.