Abstract
This article investigates an adaptive finite-time tracking control for under-actuated nonlinear systems with unknown backlash-like hysteresis and arbitrary switchings. A hierarchical sliding mode (HSM) control scheme is developed considering external disturbances and hysteresis nonlinearity. In addition, unknown functions of the considered system are handled based on neural networks (NNs) approximation, and a projection algorithm is introduced to solve the singularity of the denominator. To avoid the case in which the error is repeatedly magnified, the sum of the upper bounds of the approximation error, the external disturbance and the backlash-like hysteresis model nonlinear parts are estimated.By resorting to the Lyapunov stability theory, the boundedness of all signals can be proved under arbitrary switchings. At last, two simulation examples are presented to demonstrate the validity of the proposed approach.