Adaptive Boundary Iterative Learning Control for an Euler–Bernoulli Beam System With Input Constraint

This paper addresses the vibration control and the input constraint for an Euler-Bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance. Hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint. A restrained adaptive boundary iterative learning control (ABILC) law is proposed based on a time-weighted Lyapunov-Krasovskii-like composite energy function. In order to deal with the uncertainty of a system parameter and reject the external disturbances, three adaptive laws are designed and learned in the iteration domain. All the system states of the closed-loop system are proved to be bounded in each iteration. Along the iteration axis, the displacements asymptotically converge toward zero. Simulation results are provided to illustrate the effectiveness of the proposed ABILC scheme.