Neural network adaptive compensation control based on the backstepping method for nonlinear systems with time-varying delays

Control of nonlinear systems with time-varying delays is a common problem, particularly when the time-varying delays are unknown. This paper presents an adaptive compensation control method based on multiple neural networks. Firstly, considering the nonlinear systems with time-varying delays, a neural network method is adopted to approximate the unknown nonlinear structure with time-varying delays. On this basis, a backstepping controller is designed. Considering the unknown time-varying delays, the control effect of the neural network controller based on the backstepping method is not optimal. To deal with the problem, a double-layer adaptive compensator for the neural network is proposed. Furthermore, for the neural network adaptive compensation controller based on the backstepping method, the stability is also proved by a Lyapunov method. Finally, simulation results demonstrate the effectiveness of the scheme, especially when the nonlinear systems have an unknown time-varying delay.