Fuzzy control of nonlinear systems using rule adjustment

Abstract

A fuzzy controller design using linguistic control rule adjustment is proposed. The proposed adaptive law, which results from the direct adaptive approach, is used to indirectly regulate the output fuzzy variables in the fuzzy controller according to the prelabelled rules. The main advantage of the proposed method is that the determination of rule selection is formed by an analytical parameter equation with multiple input variables of the fuzzy controller. Practically, it is not easy to characterise the linguistic control rules and their membership function distribution without expert knowledge, especially in those cases when the input state variables of the fuzzy controller are increased. The rules are first labelled, then an adaptive law is used to tune the injected parameters in the IF-part to appropriately determine each output fuzzy variable under situations of lack of any knowledge of the plant. The derivation result shows that the proposed adaptive fuzzy controller is stable in the Lyapunov sense. Finally, a nonlinear system simulation example is applied to verify the effectiveness and the ability of the proposed fuzzy controller.