Adaptive backstepping sliding mode control for nonlinear systems with neural networks

The backstepping control is investigated for a class of unknown nonlinear systems in parametric-pure-feedback form. Neural networks(NNs) are applied to approximate the unknown dynamics. The adaptive laws of the weights of NN and the ideal sliding mode are derived in the sense of Lyapunov function, so the stability can be guaranteed. The proposed control not only relaxes the assumptions of nonlinear systems, but also holds the robustness. Moreover, the tracking error can converge to zero asymptotically. Simulations illustrate the effectiveness of the proposed approach.