Adaptive neural networks output feedback dynamic surface control design for MIMO pure-feedback nonlinear systems with hysteresis

An adaptive neural networks (NNs) output feedback tracking control approach is proposed for a class of multi-input and multi-output (MIMO) pure-feedback nonlinear systems with unknown backlash-like hysteresis and immeasurable states. Radial basis function neural networks (RBF NNs) are utilized to approximate the unknown nonlinear functions of the controlled systems, and a state observer is designed to estimate the unmeasured states. The filtered signals are introduced to circumvent algebraic loop problem encountered in the implementation of the controller, and an adaptive compensation technique are used to solve the problem of unknown backlash-like hysteresis. Based on the designed state observers, and combining the backstepping and dynamic surface control (DSC) techniques, an adaptive NN output feedback tracking control approach is developed. The proposed method not only overcomes the problem of "explosion of complexity" inherent in the backstepping control design but also guarantees that all the signals of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) and the tracking errors converge to a small neighborhood of the origin. Two simulation examples are provided to show the effectiveness of the proposed approach.