The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-184

“Analysis and Design of Fuzzy Logic Controller”

by Li-Xin Wang and Jerry M. Mendel

August 1991

In this report, the fuzzy logic controller (FLC) with product inference, centroid defuzzification, and Gaussian membership function is proven to be capable of approximating any real continuous function on a compact set to arbitrary accuracy. The Stone-Weierstrass Theorem is used as a principal tool for the analysis. Design parameters of FLC are defined, and a parallel implementation architecture for FLC is proposed. An optimal multi-input-single-output FLC is designed which can match N given input-output data pairs to arbitrary accuracy using N fuzzy rules. In order to overcome the high complexity weakpoint of the optimal FLC, a sub-optimal design method is developed. Based on the parallel architecture of FLC, the sub-optimal FLC is designed by using a new back-propagation training algorithm. This report shows that the new back-propagation FLC (BP FLC) can utilize both numerical data and linguistic rules; specifically, the BP FLC is first trained to match the given input-output data pairs using the back-propagation algorithm, then linguistic rules from human experts are added to the trained BP FLC to form the final FLC. A method of choosing the initial parameters of the BP FLC is proposed which is based on the optimal FLC; this method is shown to be very effective and makes the training for the BP FLC very fast. The BP FLC is finally applied to approximate a controller for a non-linear system. By comparing the BP FLC with the back-propagation feedforward neural network (BP FNN), this report shows that: (1) the BP FLC can be applied to any problem which is suited for the BP FNN; (2) the BP FLC can utilize both numerical and linguistic information, while the BP FNN can only utilize numerical information; and, (3) the training for the BP FLC is much faster than that for the BP FNN.

To download the report in PDF format click here: USC-SIPI-184.pdf (1.4Mb)