[1]WANG Ning,TAN Yue,WANG Dan,et al.Study on approximation capabilities of general homogenous T-S fuzzy systems[J].CAAI Transactions on Intelligent Systems,2010,5(5):436-442.[doi:10.3969/j.issn.1673-4785.2010.05.010]
Copy

Study on approximation capabilities of general homogenous T-S fuzzy systems

CAAI Transactions on Intelligent Systems[ISSN 1673-4785/CN 23-1538/TP] Volume: 5 Number of periods: 2010 5 Page number: 436-442 Column: 学术论文—人工智能基础 Public date: 2010-10-25
Title:
Study on approximation capabilities of general homogenous T-S fuzzy systems
Author(s):
WANG Ning;  TAN Yue;  WANG Dan;  WU Zhi-liang
Marine Engineering College, Dalian Maritime University, Dalian 116026, China
Keywords:
homogenous T-S fuzzy systems;  approximation capability;  complex systems;  fuzzy partition
CLC:
TP273
DOI:
10.3969/j.issn.1673-4785.2010.05.010
Abstract:
In order to analyze approximation capabilities of general homogenous T-S fuzzy systems, the general fuzzy partition (GFP) with universal significance was definitely defined in the input space of fuzzy systems through comprehensively summarizing properties of common fuzzy sets. Based on the analytical structure, a large class of general homogenous T-S fuzzy systems was proven to be able to approximate any nonlinear function to any degree of accuracy, and a sufficient condition for the introduced fuzzy systems to be the universal approximator was proposed. Concerning the degeneration of the GFP, the linear fuzzy partition (LFP) in the input space of fuzzy systems was also defined to further investigate first-order approximation capabilities of general homogenous T-S fuzzy systems. Simulation studies demonstrated that the presented theoretical results are effective and the sufficient condition was investigated to be conservative. These results provide a theoretical foundation for complex system modeling and control based on homogenous T-S fuzzy systems.
References:
［1］刘福才,陈超,邵慧,等.模糊系统万能逼近理论研究综述［J］. 智能系统学报, 2007, 2(1): 25-34.
LIU Fucai, CHEN Chao, SHAO Hui, et al. Researches for universal approximation of fuzzy systems: a survey［J］. CAAI Transactions on Intelligent Systems, 2007, 2(1): 25-34.
［2］FENG G. A survey on analysis and design of model-based fuzzy control systems［J］. IEEE Transactions on Fuzzy Systems, 2006, 14(5): 676-697.
［3］YING H. Sufficient conditions on uniform approximation of multivariate functions by general Takagi-Sugeno fuzzy systems with linear rule consequent［J］. IEEE Transactions on Systems, Man, and Cybernetics, 1998, 28(4): 515-520.
［4］ZENG Ke, ZHANG Naiyao, XU Wenli. A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators［J］. IEEE Transactions on Fuzzy Systems, 2000, 8(6): 773-780.
［5］曾珂,张乃尧,徐文立.线性T-S模糊系统作为通用逼近器的充分条件［J］.自动化学报, 2001, 27(5): 606-612.
ZENG Ke, ZHANG Naiyao, XU Wenli. Sufficient condition for linear T-S fuzzy systems as universal approximators［J］. Acta Automatica Sinica, 2001, 27(5): 606-612.
［6］曾珂,张乃尧,徐文立.典型T-S模糊系统是通用逼近器［J］.控制理论与应用, 2001, 18(2): 293-297.
ZENG Ke, ZHANG Naiyao, XU Wenli. Typical TS fuzzy systems are universal approximators［J］. Control Theory and Applications, 2001, 18(2): 293-297.
［7］刘福才,陈超,张彦柳.采样点个数对T-S模糊建模精度的影响［J］. 智能系统学报, 2008, 3(6): 541-547.
LIU Fucai, CHEN Chao, ZHANG Yanliu. The influence of sampling points on the descriptive performance of T-S fuzzy modeling［J］. CAAI Transactions on Intelligent Systems, 2008, 3(6): 541-547.
［8］王宁,孟宪尧.输入采用一般模糊划分的T-S模糊控制系统稳定性分析［J］.自动化学报, 2008, 34(11): 1441-1445.
?WANG Ning, MENG Xianyao. Stability analysis of T-S fuzzy control system with inputs using general fuzzy partition［J］. Acta Automatica Sinica, 2008, 34(11): 1441-1445.
［9］FUNTUZZI C, ROVATTI R. On the approximation capabilities of the homogenous Takagi-Sugeno model［C］//IEEE International Conference on Fuzzy Systems. New Orleans, USA， 1996: 1067-1072.
［10］TEIXEIRA M C M, ZAK S H. Stabilizing controller design for uncertain nonlinear systems using fuzzy models［J］. IEEE Transactions on Fuzzy Systems, 1999, 7(2): 133-142.
［11］WANG H O, TANAKA K, GRIFFIN M F. An approach to fuzzy control of nonlinear systems: stability and design issues［J］. IEEE Transactions on Fuzzy Systems, 1996, 4(1): 14-23.
［12］TANAKA K, IKEDA T, WANG H O. Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs［J］. IEEE Transactions on Fuzzy Systems, 1998, 6(2): 250-265.
［13］WANG H O, LI J, TANAKA K. TS fuzzy model with linear rule consequence and PDC controller: a universal framework for nonlinear control systems［J］. International Journal of Fuzzy Systems, 2003, 5(2): 106-113.
［14］王宁,孟宪尧. 齐次T-S模糊系统的逼近性能［J］.大连海事大学学报, 2007, 33(3): 36-41.
WANG Ning, MENG Xianyao. Approximation capabilities of homogeneous T-S fuzzy systems［J］. Journal of Dalian Maritime University, 2007, 33(3): 36-41.
Similar References:

Memo

-

Last Update: 2010-11-26

Copyright © CAAI Transactions on Intelligent Systems