Tuning of scaling factors in fuzzy controllers using correlation functions

The author deals with the optimal adjustment of scaling factors for fuzzy controllers (FCs). The method is based on the assumption that in the stationary case an optimally adjusted scaling factor meets a specific statistical input-output dependency. A measure for the strength of statistical dependency is the correlation function and the correlation coefficient. The adjustment of scaling factors using correlation functions is pointed out by means of a single-input-single-output (SISO) system. The correlation of the controller input and the defuzzified controller output are discussed. The computation of correlation functions and their representation inside the FC are considered. Simulation results for a system of fuzzy rules controlling a redundant robot manipulator are given