Robust adaptive control of nonlinear systems with unknown input nonlinearity

In this paper, two robust adaptive control schemes are proposed for a class of uncertain nonlinear systems in a Brunovsky form with unknown dead-zone and sector nonlinearity. 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 control gain. The novel description of input nonlinearity which makes the control system design possible is developed by introducing characteristic function and extending the definition of sector nonlinear functions. The closed-loop control system is proved to be semi-globally uniformly ultimately bounded, with the tracking error converging to zero under the condition that the sign of the control gain is known. Simulation results demonstrate the effectiveness of the approach.