Fuzzy Control Stability Analysis Using a Generalized Fuzzy Petri Net Model
Takeshi Furuhashi*, Hidehiro Yamamoto*, James F. Peters** and Witold Pedrycz**
*Dept. of Information Electronics, Nagoya University Furo-cho, Chikusa-ku, Nagoya 464-8603, Japan
**Dept. of Electrical Engineering, Univ. of Manitoba 15 Gillson Street, Winnipeg, Manitoba, Canada R3T 5V6
Fuzzy inference is used to describe nonlinear input- output relationships using fuzzy if-then rules. Continuous values of input and output are converted into granules by fuzzy sets, and each granule is labeled with a symbol. Fuzzy inference has a multigranular architecture consisting of continuous values and symbols that has worked well incorporating expert knowledge into fuzzy control. An important issue in fuzzy control is guaranteeing fuzzy control stability. We applied Petri nets to fuzzy control stability analysis and derived a theory on asymptotic stability for symbolic representation of control. We present new bridging between symbolic stability analysis and actual control behavior numerically. We use a generalized fuzzy Petri net model and its neural network representation. Conditions for validity of granularized control stability analysis are derived from the movement of tokens in neural network representation. Simulations are used to study derived conditions.
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