Time-varying Barrier Lyapunov Function Based Adaptive Neural Controller Design for Nonlinear Pure-feedback Systems with Unknown Hysteresis

This paper deals with the adaptive neural network (NN) control problem for a class of pure-feedback systems with time-varying constrained states and unknown backlash-like hysteresis. First of all, the considered plant is transferred into a strict feedback system on account of the implicit function theorem and mean value theorem. Then, the time-varying Barrier Lyapunov functions (BLFs) are integrated into the backstepping techniques so that all the states do not transgress the corresponding constraint boundary. This approach avoids the procedure of finding inverse, and therefore greatly improves the robustness of controller. At the same time, the radial basis function (RBF) NNs are employed to identify the unknown internal dynamics, which is a key operation in each step. Based on the Lyapunov stability analysis scheme, all the closed-loop signals are proved to be uniformly ultimately bounded (UUB), and the tracking error converges to a small neighborhood of the origin. Finally, two simulation examples are developed to further verify the proposed control strategy.