Control of Nonlinear Multivariable Systems Using Direct Fuzzy Learning Method

Abstract

A learning method that can acquire the control rules in the multi-input multi-output system is presented. Generally, in the control of a multivariable system, the error of the outputs must be transformed into the corrections of the inputs to get the control rules. If we do not know the mathematical modeling equation of the system, we cannot find out the Jacobian matrix to show the output variance with respect to the input variance. However, because it is not necessary to use the exact variable matrix in the learning of the fuzzy rules, this article introduces a method to get a representative constant Jacobian matrix that assures the convergence. Using this constant matrix, the fuzzy rules are successfully obtained. In particular, because many fuzzy subsets must be used in the case of a multivariable system, the optimization technique to minimize the fuzzy rule structure is also applied.