Adaptive interval type-2 fuzzy dynamic surface control for uncertain nonlinear systems with unknown asymmetric dead-zone input

In this study, an adaptive dynamic surface control (DSC) scheme based on the interval type-2 fuzzy systems is proposed for uncertain nonlinear systems with unknown asymmetric dead-zone input and unknown control gains. The dead-zone nonlinearity is represented as a time-varying system with a bounded disturbance. The proposed approach invokes the interval type-2 fuzzy system to approximate the unknown nonlinear dynamics that appears in the virtual and actual control inputs. Also, it proposes adaptive terms to compensate the effect of the disturbance-like term in the dead-zone constraint. Then, the DSC scheme is designed based on the interval type-2 fuzzy system and the dead-zone model. Adaptive laws are derived to tune the consequent parameters of the interval type-2 fuzzy system and the dead-zone model. Stability analysis of the proposed scheme shows that all the signals of the closed-loop system are uniformly ultimately bounded and the tacking error can be made arbitrary small by proper selection of the design parameters. The proposed scheme avoids the "explosion of complexity" and "singularity" problems, simultaneously. Furthermore, it can compensate the effect of the dead-zone constraint without any need to its parameters. The simulation and comparison results are presented to demonstrate the effectiveness of the proposed control scheme.