A Robust Self-Adaptive Interval Type-2 TS Fuzzy Logic for Controlling Multi-Input–Multi-Output Nonlinear Uncertain Dynamical Systems

Abstract

Recently, Type-2 fuzzy systems have become increasingly prominent as they have been applied to various nonlinear control applications. This article presents an adaptive fuzzy controller based on the sliding-mode control theory. The proposed self-adaptive interval Type-2 fuzzy controller (SAF2C) is based on the Takagi–Sugeno (TS) fuzzy model and it accommodates the “enhanced iterative algorithm with stop condition” type-reducer, which is more computationally efficient than the “Kernel–Mendel” type-reduction algorithm. We developed an integrated multi-input–multi-output (MIMO) SAF2C-controller to reduce the computation time so that we can expedite the learning process of our control algorithm by 80% compared to separate single-input–single-output (SISO) controllers. The stability of our controller is proven using the Lyapunov technique. To ensure the applicability of the presented control scheme, we implemented our controller on various nonlinear systems, including a hexacopter unmanned aerial vehicle (UAV). We also compare the accuracy of our controller with a conventional proportional–integral–derivative autopilot system. Our research indicates around 20% improvement in its transient response, in addition to achieving a better noise rejection capability with respect to a Type-1 fuzzy counterpart.