Adaptive backstepping fault-tolerant control for unmatched non-linear systems against actuator dead-zone

This study focuses on the tracking problem for a class of unmatched non-linear systems with unknown parameters and actuator dead-zone fault. The uncertainties are bounded by non-linear function with unknown parameters. Via adaptive backstepping method, a variable structure controller and a smooth controller are designed based on simplified dead-zone model with respect to actuator failure, respectively. The controllers proposed here can possess the system with excellent tracking performance. Furthermore, it is effective to avoid the chattering phenomenon that may cause damaging of controller. Finally, two numerical examples, in which a practical wastewater treatment system is considered, are given to show the effectiveness of the proposed control methods.