Solving Sylvester equation is a common algebraic problem in mathematics and control theory. Different from the traditional fixed-parameter recurrent neural networks, such as gradient-based recurrent neural networks or Zhang neural networks, a novel varying-parameter recurrent neural network, [called varying-parameter convergent-differential neural network (VP-CDNN)] is proposed in this paper for obtaining the online solution to the time-varying Sylvester equation. With time passing by, this kind of new varying-parameter neural network can achieve super-exponential performance. Computer simulation comparisons between the fixed-parameter neural networks and the proposed VP-CDNN via using different kinds of activation functions demonstrate that the proposed VP-CDNN has better convergence and robustness properties.

中文翻译：

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时变Sylvester方程在线求解的新型变参数递归神经网络


求解西尔维斯特方程是数学和控制理论中常见的代数问题。与传统的固定参数循环神经网络（例如基于梯度的循环神经网络或Zhang神经网络）不同，一种新颖的变参数循环神经网络[称为变参数收敛差分神经网络（VP-CDNN）]是本文提出用于获得时变西尔维斯特方程的在线解。随着时间的推移，这种新型变参数神经网络可以实现超指数性能。通过使用不同类型的激活函数对固定参数神经网络和所提出的 VP-CDNN 进行计算机仿真比较，表明所提出的 VP-CDNN 具有更好的收敛性和鲁棒性。