Structured Learning and Decomposition of Fuzzy Models for Robotic Control Applications
Journal of Intelligent and Robotic Systems
Implementation of Nonlinear Fuzzy Models Using Microcontrollers
AFSS '02 Proceedings of the 2002 AFSS International Conference on Fuzzy Systems. Calcutta: Advances in Soft Computing
Hierarchical TS fuzzy system and its universal approximation
Information Sciences—Informatics and Computer Science: An International Journal
Kernel shapes of fuzzy sets in fuzzy systems for function approximation
Information Sciences: an International Journal
Stable indirect adaptive control based on discrete-time T--S fuzzy model
Fuzzy Sets and Systems
An optimal T-S model for the estimation and identification of nonlinear functions
WSEAS Transactions on Systems and Control
New optimal approach for the identification of Takagi-Sugeno fuzzy model
CONTROL'08 Proceedings of the 4th WSEAS/IASME international conference on Dynamical systems and control
Approximation properties of piece-wise parabolic functions fuzzy logic systems
Fuzzy Sets and Systems
Approximation of stochastic processes by T--S fuzzy systems
Fuzzy Sets and Systems
An adaptive fuzzy observer-based approach for chaotic synchronization
International Journal of Approximate Reasoning
Nonlinear identification and adaptive control based on self-structuring fuzzy systems
FUZZ-IEEE'09 Proceedings of the 18th international conference on Fuzzy Systems
International Journal of Applied Mathematics and Computer Science - Special Section: Robot Control Theory Cezary Zielinski
Multiple incremental fuzzy neuro-adaptive control of robot manipulators
IROS'09 Proceedings of the 2009 IEEE/RSJ international conference on Intelligent robots and systems
An anti-windup design for T-S fuzzy time-delay systems with saturating inputs
FSKD'09 Proceedings of the 6th international conference on Fuzzy systems and knowledge discovery - Volume 6
Analysis and design of time-variant fuzzy systems based on dynamic fuzzy inference
Computers & Mathematics with Applications
An affine fuzzy model with local and global interpretations
Applied Soft Computing
Information Sciences: an International Journal
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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