Anti-interference Zeroing Neural Network Model for Time-Varying Tensor Square Root Finding

Square root finding plays an important role in many scientific and engineering fields, such as optimization, signal processing and state estimation, but existing research mainly focuses on solving the time-invariant matrix square root problem. So far, few researchers have studied the time-varying tensor square root (TVTSR) problem. In this study, a novel anti-interference zeroing neural network (AIZNN) model is proposed to solve TVTSR problem online. With the activation of the advanced power activation function (APAF), the AIZNN model is robust in solving the TVTSR problem in the presence of the vanishing and non-vanishing disturbances. We present detailed theoretical analysis to show that, with the AIZNN model, the trajectory of error will converge to zero within a fixed time, and we also calculate the upper bound of the convergence time. Numerical experiments are presented to further verify the robustness of the proposed AIZNN model. Both the theoretical analysis and numerical experiments show that, the proposed AIZNN model provides a novel and noise-tolerant way to solve the TVTSR problem online.