Compactness of Family of Fuzzy Sets in L2 Space with Application to Optimal Control
Summary :
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.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E92-A No.4 pp.952-957
- Publication Date
- 2009/04/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1587/transfun.E92.A.952
- Type of Manuscript
- Special Section PAPER (Special Section on Advanced Technologies Emerging Mainly from the 21st Workshop on Circuits and Systems in Karuizawa)
- Category
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Takashi MITSUISHI, Yasunari SHIDAMA, "Compactness of Family of Fuzzy Sets in L2 Space with Application to Optimal Control" in IEICE TRANSACTIONS on Fundamentals,
vol. E92-A, no. 4, pp. 952-957, April 2009, doi: 10.1587/transfun.E92.A.952.
Abstract: 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.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E92.A.952/_p
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@ARTICLE{e92-a_4_952,
author={Takashi MITSUISHI, Yasunari SHIDAMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Compactness of Family of Fuzzy Sets in L2 Space with Application to Optimal Control},
year={2009},
volume={E92-A},
number={4},
pages={952-957},
abstract={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.},
keywords={},
doi={10.1587/transfun.E92.A.952},
ISSN={1745-1337},
month={April},}
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TY - JOUR
TI - Compactness of Family of Fuzzy Sets in L2 Space with Application to Optimal Control
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 952
EP - 957
AU - Takashi MITSUISHI
AU - Yasunari SHIDAMA
PY - 2009
DO - 10.1587/transfun.E92.A.952
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E92-A
IS - 4
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - April 2009
AB - 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.
ER -
English
