Adaptive neural network control for pure-feedback nonlinear time delay systems with triangular control structure

In this paper, adaptive neural network control is investigated for a class of nonlinear systems under the effects of time delay and uncertain nonlinear functions. The system is described in form of pure-feedback and triangle structure, and the virtual control law is proposed to solve the mismatch problem. The unknown functions are approximated by adaptive neural networks and the weights of the neural network are iteratively and adaptively updated through the system state. To overcome the controller singular problem, integral-type Lyapunov function is utilized, the closed-loop control system is proved to be semiglobally uniformly ultimately bounded (SGUUB). A number of bench mark tests are simulated to demonstrate the effectiveness of the proposed approach.