Controller design using multigranular architecture of fuzzy inference and Petri nets

Fuzzy inference is a method to describe nonlinear input-output relationships using fuzzy if-then rules. Continuous values of the inputs and outputs 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, and this architecture has worked well to incorporate experts´ know-how into fuzzy controls. One of the important problems of fuzzy control is to guarantee stability of the fuzzy control system. The authors have applied Petri nets to the stability analysis of the fuzzy control system. A theory of asymptotic stability has been derived for the symbolic representation of the control system. The paper presents a new method to bridge between the stability analysis on the symbolic level and the actual behavior of the control system on the numerical level. The new method uses a generalized fuzzy Petri net model and its neural network representation. The paper introduces a guideline for designing a fuzzy control system which guarantees the validity of the stability analysis on the symbolic representation of the control system