Neural network based boundary control of a vibrating string system with input deadzone

In this paper, a boundary control scheme is developed for a vibrating flexible string system subject to input deadzone and external disturbance. First, a basic boundary control scheme is proposed to suppress the string's vibration based on the backstepping method. Subsequently, a radial basis function neural network (RBFNN) is utilized to handle the effect of the input deadzone and a disturbance observer is exploited to track the external disturbance. Under the proposed control, the uniformly ultimately bounded stability of the closed loop system is achieved through rigorous Lyapunov analysis without any discretization or simplification of the dynamics in the time and space. Finally, simulation results are demonstrated for control performance verification.