Asymptotic tracking control of uncertain nonlinear systems with unknown actuator nonlinearity and unknown gain signs

Two adaptive control schemes for a class of uncertain nonlinear systems preceded by actuator nonlinearity are presented. We consider two possible input nonlinearities, that is, backlash-like hysteresis and symmetric dead-zone, which can be simultaneously dealt with by using the proposed compensation controllers. The knowledge on the signs of the unknown plant parameters and the parameters in the input nonlinearity models is not required. Only the boundedness of the reference signal is assumed. The Nussbaum gain approach is employed to remove the assumption on the control gain sign. The first scheme is based on the backstepping technique. The final step of the recursive design is crucial for the closed-loop stability. In the second scheme, a direct adaptive control law is designed. The controller has a simple structure and only one adaptation parameter is updated. In both controllers, it is shown that asymptotic tracking is ensured. Two numerical examples are provided to show the effectiveness of the theoretical results.