Anti-Disturbance Boundary Control for a Wave Equation with Input Disturbance

In this article, we investigate the exponential stabilization issue of a wave equation with the external input disturbance, which is described by a nonlinear exogenous system. A novel disturbance observer is constructed to estimate the unknown input disturbance. Then, based on the proposed disturbance observer, a boundary control strategy is developed to cancel the effect of disturbance and stabilize the system. The exponential stability is proven by employing the Lyapunov’s direct method. This method can be extended to a class of flexible systems described by the hyperbolic partial differential equation met in the practical engineer area. The example of a nonuniform flexible string system is given, where the effectiveness of the proposed strategy is evaluated based on simulations.