Robust adaptive neural control of SISO nonlinear systems with unknown dead-zone and completely unknown control gain

In this paper, robust adaptive neural tracking control is developed for a class of uncertain SISO nonlinear systems in a Brunovsky form with unknown nonlinear dead-zone and unknown control gain & its sign. The design is based on the principle of sliding mode control and the use of Nussbaum-type function in solving the problem of the completely unknown function control gain. A novel description of general nonlinear dead-zone, which makes the control system design possible, is introduced by using the mean value theorem. The approach removes the condition of the equal slope with defined region for the dead-zone. By utilizing the integral-type Lyapunov function and introducing an adaptive compensation for the upper bound of the optimal approximation error and the dead-zone disturbance, the closed-loop control system is proved to be semi-globally uniformly ultimately bounded