Compactness of Family of Fuzzy Sets in L2 Space with Application to Optimal Control

Takashi MITSUISHI  Yasunari SHIDAMA  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E92-A   No.4   pp.952-957
Publication Date: 2009/04/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E92.A.952
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Advanced Technologies Emerging Mainly from the 21st Workshop on Circuits and Systems in Karuizawa)
fuzzy control,  L2 space,  variation problem,  feedback control,  approximate reasoning,  

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The optimization of nonlinear feedback fuzzy system using the product-sum-gravity method is described in this paper. The fuzzy control discussed here is the nonlinear feedback control in which the feedback laws are determined by IF-THEN type fuzzy production rules through product-sum-gravity method. To prove existence of optimal control, we applied compactness of a set of membership functions in L2 space and continuity of the approximate reasoning, and prepared some propositions concerning product-sum-gravity method. By considering fuzzy optimal control problems as problems of finding the minimum (maximum) value of the integral cost (benefit) function on an appropriate set of membership functions, the existence of fuzzy optimal control is shown.