Neural Networks-based Adaptive Backstepping Super-twisting Sliding Mode Control of Uncertain Nonlinear Systems with Unknown Hysteresis

An adaptive neural network output feedback tracking control scheme is proposed for uncertain nonlinear systems with unknown hysteresis, unmeasurable states, and external disturbances. Radial basis function neural networks (RBFNNs) are used to approximate the unknown nonlinear functions, and a neural network state observer (NNSO) and a nonlinear disturbance observer (NDO) are designed to estimate the unmeasurable states and unknown compounded disturbances, respectively. Based on the NNSO and NDO, and combing the backstepping technique and super-twisting algorithm, a neural networks-based adaptive backstepping super-twisting sliding mode control (NNABSTSMC) scheme is proposed without constructing the hysteresis inverse. The problem of “explosion of complexity” inherent in the backstepping method is eliminated by using dynamic surface control (DSC) technique. The presented controller not only guarantees that all signals of the controlled system are semi-globally ultimately uniformly bounded (SUUB) via the Lyapunov analysis method, but also ensures that the observer and tracking errors fast converge to a neighborhood of the origin. A numerical example is provided to demonstrate the effectiveness of the proposed control scheme.