Revisiting Zeroing Neural Networks: An Optimization Perspective

Zeroing neural networks (ZNNs) serve as neurodynamic solvers for time-varying optimization. However, their conventional first-order gradient descent nature causes high-gain instability and tracking lags under dynamic disturbances. To address this issue, we propose a unified second-order dynamical framework, which includes two canonical forms: 1) the momentum-enhanced noise-tolerant ZNN (ME-NTZNN); and 2) the Nesterov-enhanced noise-tolerant ZNN (NE-NTZNN). Theoretical analyses indicate that the ME-NTZNN utilizes explicit physical damping to suppress underdamped oscillations, whereas the predictive mechanism in the NE-NTZNN induces virtual damping and virtual stiffness to reduce dynamic tracking lags. We prove the global uniform ultimate boundedness (GUUB) and robust stability of these architectures. Additionally, we conduct computational complexity and parameter sensitivity analyses to evaluate their implementation feasibility. Evaluations on dynamic quadratic benchmarks show that the proposed solvers reduce steady-state residual errors compared with first-order baselines. Finally, real-time kinematic control experiments on a 7-degree-of-freedom Franka redundant robotic arm validate the practicability of the proposed neurodynamic framework.