Adaptive RBF neural-networks control for a class of time-delay nonlinear systems

A control scheme combined with backstepping, radius basis function (RBF) neural networks and adaptive control is proposed for the stabilization of nonlinear system with input and state delay. By using state transformation, the original system is converted to the system without input delay. The RBF neural network is employed to estimate the unknown continuous function. The controller is designed for the converted system so that the closed-loop system is bounded. According to the relation between the original system and the converted one, the state of the original system is proved to be bounded. The control scheme ensures that the closed-loop system is semi-globally uniformly ultimately bounded.