Recursive neural networks are generally divided into dynamic neural networks and static neural networks to refer to the neural networks with one or more feedback links in the network structure. Inevitably, there exist some problems such as poor approximation performance and poor stable convergence performance due to complex network structure. The noise-tolerant gradient-oriented neurodynamic (NTGON) model proposed in this study is an improved model based on the traditional idea of a gradient neural network (GNN) model. The proposed NTGON model can obtain accurate and efficient results under the condition of various noises when computing the Sylvester equation, which is effectively used to solve various problems with noise pollution that are frequently encountered in practical engineering. Compared with the original GNN model for the Sylvester equation, the NTGON model exponentially converges to the theoretical solution starting from any initial state. It is demonstrated that the noise-polluted NTGON model converges to the theoretical solution globally no matter how large the unknown matrix-form noise is. Furthermore, simulation results show that the proposed NTGON model achieves a performance that is superior to that of the original GNN model for solving the Sylvester equation in the presence of noise.

递归神经网络一般分为动态神经网络和静态神经网络，是指在网络结构中具有一个或多个反馈环节的神经网络。由于网络结构复杂，不可避免地存在逼近性能差、稳定收敛性能差等问题。本研究提出的抗噪声梯度导向神经动力学（NTGON）模型是基于梯度神经网络（GNN）模型传统思想的改进模型。提出的NTGON模型在计算Sylvester方程时能够在各种噪声条件下获得准确高效的结果，有效地用于解决实际工程中经常遇到的各种噪声污染问题。与 Sylvester 方程的原始 GNN 模型相比，NTGON 模型从任何初始状态开始都呈指数收敛到理论解。结果表明，无论未知矩阵形式的噪声有多大，受噪声污染的 NTGON 模型都能全局收敛到理论解。此外，仿真结果表明，在存在噪声的情况下，所提出的 NTGON 模型在求解 Sylvester 方程方面的性能优于原始 GNN 模型。