Direct adaptive general type‐2 fuzzy control for a class of uncertain non‐linear systems

Abstract

In this study, a stable direct adaptive general type-2 fuzzy logic controller (DAG2FLC) is introduced for a class of non-linear systems. The proposed controller uses advantages of general type-2 fuzzy logic systems (GT2FLSs) in handling dynamic uncertainties to approximate unknown non-linear actions. Implementing general type-2 fuzzy systems is computationally costly; however, by using a recently introduced α-plane representation, a GT2FLS can be seen as composition of several interval type-2 fuzzy logic systems with a corresponding level of α for each. Linguistic rules are directly incorporated into the DAG2FLC controller and a H ∞ compensator is added to attenuate external disturbance and fuzzy approximation error. Also general type-2 fuzzy adaptation laws are derived using Lyapunov approach, and the stability of the closed-loop system has been proven by mathematical analysis. In order to evaluate the performance of the proposed controller, the results are compared with those obtained by direct adaptive type-1 fuzzy logic controller and a direct adaptive interval type-2 fuzzy logic controller, which are the latest researches in the problem in hand. The proposed controller is applied to a chaotic Gyro system as a case study. Simulation reveals the effectiveness of the proposed controller in presence of dynamic uncertainties and external disturbances.