Approximation-based Adaptive NN Control for Nonstrict-Feedback Nonlinear Systems with Input Delay

This paper focuses on the problem of adaptive neural network (NN) control for a class of nonstrict-feedback nonlinear systems with input delay. A novel auxiliary system is introduced to compensate the input delay. The variable separation technique is utilized to overcome the difficulty from the nonstrict-feedback structures. Furthermore, Barrier Lyapunov Functions (BLFS) are employed to ensure that the unknown functions remain within a given compact superset where the NN approximation is valid. With the aid of NN approximation method and backstepping technique, an adaptive NN controller is designed which can guarantee all the states in the closed-loop systems are semi-globally uniformly ultimately bounded. The stability of the closed- loop system are proved by using the Lyapunov stability theorem and a simulation example is given to illustrate the effectiveness of the proposed method.