Robust neural dynamics with adaptive coefficient applied to solve the dynamic matrix square root

Abstract

Abstract Zeroing neural networks (ZNN) have shown their state-of-the-art performance on dynamic problems. However, ZNNs are vulnerable to perturbations, which causes reliability concerns in these models owing to the potentially severe consequences. Although it has been reported that some models possess enhanced robustness but cost worse convergence speed. In order to address these problems, a robust neural dynamic with an adaptive coefficient (RNDAC) model is proposed, aided by the novel adaptive activation function and robust evolution formula to boost convergence speed and preserve robustness accuracy. In order to validate and analyze the performance of the RNDAC model, it is applied to solve the dynamic matrix square root (DMSR) problem. Related experiment results show that the RNDAC model reliably solves the DMSR question perturbed by various noises. Using the RNDAC model, we are able to reduce the residual error from 10 $$^1$$ 1 to 10 $$^{-4}$$ - 4 with noise perturbed and reached a satisfying and competitive convergence speed, which converges within 3 s.

Keywords

• Dynamic matrix square root
• Time-dependent
• Zeroing neural network
• Adaption coefficient