An adaptive gradient compensation neural network for time-varying nonlinear optimization with application to redundant manipulators

Gradient neural networks (GNNs) provide an effective approach for solving time-varying nonlinear optimization (TVNO) problems but suffer from inherent lagging errors. Existing GNN acceleration methods generally strengthen feedback correction without explicitly compensating for the drift induced by time variation and often face a trade-off between convergence speed and numerical stability. To address these limitations, this paper proposes an adaptive gradient compensation neural network (AGCNN). It integrates a feedforward velocity compensation mechanism to explicitly compensate for the drift induced by time variation and an adaptive spectral compensation mechanism to enhance feedback correction under weak-curvature conditions; together, the two mechanisms eliminate the inherent lagging error of GNNs. An enhanced power-exponential magnitude activation function (EPMAF) is further developed to improve convergence performance and robustness to noise. Theoretical analysis establishes global finite-time convergence and robustness under bounded disturbances, with explicit bounds on convergence time and steady-state error. Numerical results show that AGCNN achieves convergence times on the order of 10^-3-10^-2 s and maintains the maximum steady-state residual error on the order of 10^-4-10^-3 under different noise conditions. Experiments on a Franka Emika Panda manipulator further validate its effectiveness, with maximum position errors on the order of 10^-4 m.