Adaptive Neural Boundary Control of a Rotating Flexible Beam with Input Dead-Zone and Output Constraint

This paper addresses the adaptive neural network-based boundary control problem for a rotating flexible beam system (RFBS) subject to unknown distributed and boundary disturbances, input dead-zone nonlinearity, and parametric uncertainties. The system is composed of a flexible beam with one end fixed to the center of a rotating disk, the other end is attached to a tip mass. The system is governed by coupled partial and ordinary differential equations (PDEs–ODEs), presenting significant challenges due to its infinite-dimensional nature. To achieve simultaneous vibration suppression and strict enforcement of boundary output constraints, a novel adaptive boundary control scheme is developed. The proposed controller incorporates a barrier Lyapunov function (BLF) to handle output constraints, radial basis function (RBF) neural networks to compensate for unknown system dynamics and dead-zone effects, and a disturbance estimator to reject boundary perturbations. By constructing a composite Lyapunov function candidate, the uniform ultimate boundedness (UUB) of the closed-loop system is proved via Lyapunov stability analysis. Numerical simulations are conducted to illustrate the effectiveness of the proposed control approach.