A control scheme for a class of uncertain nonlinear systems with state delay and actuator dead-zone

The control problem of a class of uncertain nonlinear systems which is with state delay and actuator dead-zone together is studied in this paper. The controller is derived step by step through a backstepping procedure, where an adaptive fuzzy logic system is employed to approximate the unknown functions encountered. By introducing hyperbolic tangent functions, both the effects of state delay and the actuator dead-zone are compensated by the controller. Different from the existing results for unknown nonlinear delay systems, the proposed scheme can guarantee the desired control objective in the presence of actuator dead-zone. However, unlike the existing dead-zone compensation strategy where the dead-zone is treated as the sum of a linear function and a bounded disturbance-like term, this scheme reduces the bound of the latter by appropriate decomposing. Thus the additional robust control effort used to deal with the disturbance-like term can be saved effectively. It is proved in theory that the closed-loop system is semi-globally uniformly ultimately stable and its output can track the reference signal as closely as possible. Finally, a simulation example is employed to demonstrate the effectiveness of the control scheme.