Backstepping Technology-Based Adaptive Boundary ILC for an Input–Output-Constrained Flexible Beam

This article focuses on vibration suppression of an Euler–Bernoulli beam which is subject to external disturbance. By integrating backstepping technique, an adaptive boundary iterative learning control (ABILC) is put forward to suppressing vibration. The adaptive law is proposed for handing the parameter uncertainty and the iterative learning term is designed to deal with periodic disturbance. An auxiliary system is utilized to compensate the effect of input nonlinearity. In addition, a barrier Lyapunov function is adopted to deal with asymmetric output constraint. With the proposed control strategy, the stability of the closed-loop system is proven based on rigorous Lyapunov analysis. In the end, the effectiveness of the proposed control is illustrated through numerical simulation results.