IEEE Trans Cybern. 2018 Nov;48(11):3135-3148. doi: 10.1109/TCYB.2017.2760883. Epub 2018 Feb 8.
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.
求解 Sylvester 方程是数学和控制理论中的一个常见代数问题。与传统的固定参数递归神经网络（如基于梯度的递归神经网络或 Zhang 神经网络）不同，本文提出了一种新的变参数递归神经网络，称为变参数收敛微分神经网络（VP-CDNN），用于获得时变 Sylvester 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，在固定参数神经网络和所提出的 VP-CDNN 之间进行计算机模拟比较，结果表明所提出的 VP-CDNN 具有更好的收敛性和鲁棒性。
