RBFNN-Based Boundary Control for Disturbance Attenuation of Flexible Beams Under Fixed-Joint Actuation

This work addresses the boundary disturbance attenuation problem for a flexible beam governed by a fourth-order partial differential equation. A boundary disturbance observer based on a radial basis function neural network is proposed to achieve high-accuracy online estimation of disturbances without prior knowledge of the disturbance dynamics. In addition, a boundary feedback controller acting only at the fixed end is designed. The control objectives are to ensure accurate tracking of the desired angular position, suppress elastic vibrations, and attenuate the influence of unknown time-varying boundary disturbances. By constructing a Lyapunov functional, the stability of the closed-loop system is established. Numerical simulations demonstrate the effectiveness of the proposed observer and control law.