Adaptive Neural Network-Based Tracking Control for a Single-Link Flexible Manipulator Under State Constraints

Flexible manipulators have attracted increasing attention due to their lightweight structure, high flexibility, and energy efficiency, for which they are suitable for delicate and high-precision tasks. However, their control remains a problem because of strong nonlinearities and uncertainties in the system. Based on the trajectory tracking control problem of the single-link flexible manipulator (SLFM) system, this paper proposes a fractional order adaptive neural network control scheme for SLFM under symmetric time-varying full-state constraints. Firstly, a fractional-order dynamic model is established to better capture the inherent memory and nonlinear characteristics of the SLFM. Secondly, an adaptive radial basis function (RBF) neural network-based control scheme is developed within a backstepping framework, and a symmetric time-varying barrier Lyapunov function (BLF) is incorporated to guarantee that all system states remain within predefined bounds. In addition, command filters are introduced to avoid the "explosion of complexity" caused by backstepping. Next, theoretical analysis based on Lyapunov stability theory is provided to demonstrate that all signals in the closed-loop system are bounded, while the tracking error converges to a small neighborhood of zero. Finally, the proposed method is applied as an SLFM: the simulation results show that the presented controller has excellent control performance, the tracking error is less than 0.02 rad, and the tip polarization angle of the system does not exceed 0.045 rad. Additionally, the comparison with the recent DSC and SMC methods also shows that the designed controller behaves with less tracking error, which in return validates the effectiveness and superiority of the proposed control strategy.