A fractional-order fixed-time attractive and noise-tolerant zeroing neural network and its application to robotic...

Real-time and high-precision solving of time-varying problems is of great significance in fields such as robotic control and signal processing. As an efficient online method for solving time-varying problems, the Zeroing neural network (ZNN) has been extensively investigated. However, traditional integer-order ZNN models have inherent limitations in shaping convergence dynamics and accommodating non-local memory effects. To address these issues, a fractional-order fixed-time attractive and noise-tolerant Zeroing neural network (FO-FTNTZNN) is proposed, and its fixed-time attractivity in the Mittag-Leffler sense under noise-free conditions and its robust stability under bounded noise disturbances are rigorously demonstrated using a non-smooth fractional-order Lyapunov function. Furthermore, the attraction characteristics and anti-interference performance of the FO-FTNTZNN in both noise-free and noisy environments are further verified by multiple sets of numerical simulation experiments. Finally, the proposed FO-FTNTZNN model is successfully applied to the trajectory tracking control problem of a robotic manipulator. In summary, the proposed FO-FTNTZNN model provides a unified fractional-order framework for time-varying problem solving and robotic control, integrating fixed-time attractivity and bounded-noise robustness, and demonstrates its practical potential through numerical simulations and robotic trajectory tracking. A fractional-order parameter analysis is further provided as a supporting sensitivity study to characterize the memory-dependent dynamic behavior and transient response of the proposed framework.