Solving time-varying linear equation and inequality (TVLEI) problem has attracted extensive attention in numerous scientific and engineered fields. In this article, it is basically considered that the commonly used dynamics neural network in the virtual environment is inevitably interfered with by the variable measurement noises while dealing with the TVLEI problem. An adaptive enhanced and noisesuppressing zeroing neural network (AENSZNN) model is proposed as an improved algorithm for solving the TVLEI problem. An adaptive scale factor based on the residual error norm is designed to make the proposed AENSZNN model converge to the theoretical solution faster. Furthermore, the momentum enhancement terms added to the model enables the AENSZNN model to effectively solve the TVLEI problem in real-time under the obstruction of different measurement noises. Besides, theoretical results and numerical experiments indicate that the AENSZNN model has advantages in convergence accuracy and robustness to noises compared with the existing algorithms. Note that, the proposed AENSZNN model is successfully exploited for the estimation of mobile object localization.
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.
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