A neural network adaptive backstepping high-order terminal sliding mode control scheme is proposed for a
class of uncertain nonlinear systems with mismatched uncertainties. At the first ?? − 1 steps, neural networks are employed
to approximate the unknown nonlinear functions and the dynamic surface control is combined with backstepping design
technique to design the virtual controller, so that the explosion of complexity in traditional backstepping design is avoided
and mismatched uncertainties are restrained perfectly. In the ??-th step, the high-order sliding mode control law is designed
by combining with the non-singular terminal sliding mode to eliminate the chattering and make the system robust to both
matched and mismatched uncertainties. By theoretical analysis, all the states in the closed loop systems are guaranteed to be
semi-globally uniformly ultimately bounded. Finally, the simulation results show the effectiveness of the proposed method.