DNA genetic algorithm for design of the generalized membership-type Takagi-Sugeno fuzzy control system

We propose a new DNA-based genetic algorithm (DNA-GA) to optimize the design parameters of a generalized membership-type Takagi-Sugeno fuzzy controller (GTSFC). The GTSFC employs TS fuzzy rules with linear consequent, e^-|ax+b|(c)-type input fuzzy sets containing almost arbitrary continuous input fuzzy sets, Zadeh fuzzy logic AND operation, and the widely-used centroid defuzzier. The GTSFC is proved to be a nonlinear PI controller with variable gains. The optimized design parameters are the input fuzzy sets and the linear consequent of the rules. The DNA-GA uses a DNA encoding method stemmed from the structure of the biological DNA to encode the design parameters of the GTSFC. The genetic operators of the method are based on the DNA genetic operations. The encoding method can significantly shorten the code length of DNA chromosomes and is suitable for complex knowledge representation. As a demonstration, we show how to implement the new method to optimize the design parameters of the GTSFC to control a nonlinear system. Computer simulation results indicate that the performance of the designed fuzzy controller is satisfactory