In this paper, a neural-network-based adaptive backstepping control scheme is developed for a class of unknown nonlinear systems with unknown time-varying delayed states and unknown saturated delayed input. In the proposed method, radial basis function neural network is adopted to approximate the unknown nonlinear functions. An adaptive backstepping design is employed to compensate for the unknown time-varying delays in states. In addition, to overcome the effects of input delay, an auxiliary dynamic system is constructed. Moreover, a novel adaptive law is used for estimating unknown bounds of saturation function. Using the Lyapunov stability theorem, it is proven that the closed-loop system is semi-globally uniformly ultimately bounded and the tracking error can converge to small desired value by the proper choose of design parameters. Finally, the effectiveness of the proposed method is illustrated by applying it to a chemical reactor recycle system, one-link manipulator actuated by a DC motor and a Brusselator model.
