EXPLICIT FUNCTIONS OF FUZZY CONTROL SYSTEMS

1996 ◽  
Vol 04 (06) ◽  
pp. 515-535 ◽  
Author(s):  
LÁSZLÓ T. KÓCZY ◽  
MICHIO SUGENO
Keyword(s):  
Computational Complexity ◽  
Fuzzy Control ◽  
Control Systems ◽  
Mathematical Description ◽  
Membership Functions ◽  
Mathematical Functions ◽  
Low Computational Complexity ◽  
Special Cases ◽  
Single Input ◽  
Explicit Formulae

Fuzzy control systems have proved their applicability in many areas. Their user-friend-liness and transparency certainly belong to their main advantages, and these two enable developing and tuning such controllers easily, without knowing their exact mathematical description. Nevertheless, it is of interest to know, what mathematical functions hide behind a set of fuzzy rules and an inference machine. For practical purposes it is necessary to consider real, implementable fuzzy control systems with reasonably low computational complexity. This paper discusses the problem of what types of functions are generated by realistic fuzzy control systems. In the paper the explicit formulae of the transference functions for practically important special cases are determined, controllers having rules with triangular and trapezoidal membership functions, and crisp consequents. Here we restrict our investigations to rules with a single input.

A New Fuzzy Inference Method for Symbolic Stability Analysis of Multigranular Intelligent Control System

2000 ◽  
Vol 12 (6) ◽  
pp. 664-674
Author(s):  
Hidehiro Yamamoto ◽  
◽  
Takeshi Furuhashi
Keyword(s):  
Control System ◽  
Stability Analysis ◽  
Fuzzy Control ◽  
Control Systems ◽  
Fuzzy Inference ◽  
Continuous System ◽  
Asymptotically Stable ◽  
Membership Functions ◽  
Symbolic System ◽  
Inference Method

Fuzzy inference has a multigranular architecture consisting of symbols and continuous values, and has worked well to incorporate experts' know-how into fuzzy controls. Stability analysis of fuzzy control systems is one of the main topics of fuzzy control. A recently proposed stability analysis method on the symbolic level opened the door to the design of stable fuzzy controller using symbols. However the validity of the stability analysis in the symbolic system is not guaranteed in the continuous system. To guarantee this validity, a nonseparate condition has been introduced. If the fuzzy control system is asymptotically stable in the symbolic system and the system satisfies the nonseparate condition, the continuous system is also asymptotically stable. However this condition is too conservative. The new condition called a relaxed nonseparate condition has been proposed and the class of control systems with guaranteed discretization has been expanded. However the relaxed condition has been applicable only to controf systems having symmetric membership functions. This paper presents a new fuzzy inference method that makes the relaxed condition applicable to fuzzy control systems with asymmetric membership functions. Simulations are done to demonstrate the effectiveness of the new fuzzy inference method. The proof of the expansion of the relaxed nonseparate condition is also given.

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