Adaptive control using interval type-2 fuzzy logic

Type-2 (T2) fuzzy systems have gained increasing attention in the recent years. There have been a number of T2 fuzzy control studies in the literature but only one of them is involved in adaptive control. The objective of this paper is to develop a new and theoretically rigorous interval T2 adaptive fuzzy controller for controlling uncertain systems. Our adaptive controller contains a T2 fuzzy system component that is mathematically proven to be capable of approximating any continuous function to any degree of accuracy (in contrast, the sole work in the literature just assumes the universal approximation ability without showing any proof). Based on the Lyapunov method, we design the adaptive laws with mathematical proofs for stability and convergence of the closed-loop system. The controller updates its parameters online to control an uncertain system and track a reference trajectory. Our simulation study involves a nonlinear inverted pendulum. The simulation results demonstrate that the interval T2 adaptive fuzzy controller can achieve the system stability as designed and maintain good tracking performance. We also use the simulation to study the system performance under noise and disturbance.