A combined multiple sliding mode and backstepping design to robust adaptive neural control for uncertain nonlinear systems

A robust adaptive neural-based multiple sliding mode backstepping control scheme is proposed for a general class of nonlinear systems in strict feedback form with unknown nonlinearities and uncertain disturbances in this paper. In the controller design procedure, the RBF neural networks are employed to approximate the unknown part of the virtual controller, thus the explosion of complexity in traditional backstepping design caused by repeated differentiations of virtual controller and the controller singularity problem are avoided perfectly. The influence of the modelling and parameter estimation errors are minimized by introducing the adaptive compensation term for the unknown upper bound of both neural networks approximation error and uncertain disturbances. All the signals in the closed-loop system are guaranteed to be semi-globally uniformly ultimately bounded. Simulation results demonstrate the effectiveness of the proposed scheme.