A class of general type-2 fuzzy controller based on adaptive alpha-plane for nonlinear systems[Formula presented]

This study introduces a general type-2 Takagi–Sugeno–Kang fuzzy controller (GT2-TSKFC) for controlling uncertain systems. The proposed GT2-TSKFC uses equidistant type-2 triangular membership functions (MFs) for the antecedents, Larsen's implication method, type-1 fuzzy sets for the consequent parameters, and a direct defuzzification method. The analytical structure of the proposed controller indicates that the alpha-plane and apex of the secondary MFs have a noticeable effect on calculating the control signal. Adaptation of the alpha-plane and apex of the secondary MFs is performed using the Lyapunov function to achieve the stability of the controlled system. The proposed controller is applied to an uncertain nonlinear inverted pendulum system. The results of the proposed control algorithm are compared with those of a general type-2 fuzzy controller with a specific number of alpha-planes, a quasi type-2 fuzzy controller, an interval type-2 fuzzy controller, and a type-1 fuzzy controller to demonstrate the robustness and effectiveness of the proposed scheme.