Zhang Zhijun, Zheng Lunan
IEEE Trans Cybern. 2019 Oct;49(10):3627-3639. doi: 10.1109/TCYB.2018.2841970. Epub 2018 Jun 14.
A novel recurrent neural network, which is named as complex varying-parameter convergent-differential neural network (CVP-CDNN), is proposed in this paper for solving the time-varying complex Sylvester equation. Two kinds of CVP-CDNNs (i.e., CVP-CDNN Type I and Type II) are illustrated and proved to be effective. The proposed CVP-CDNNs can achieve super-exponential performance if the linear activation function is used. Some activation functions are considered for searching the better performance of the CVP-CDNN and the finite time convergence property of the CVP-CDNN with sign-bi-power activation function is testified. The convergence time of the CVP-CDNN with sign-bi-power activation function is shorter than complex fixed-parameter convergent-differential neural network (CFP-CDNN). Moreover, compared with traditional CFP-CDNN, better convergence performances of novel CVP-CDNN are verified by computer simulation comparisons.
本文提出了一种新型递归神经网络，称为复变参数收敛微分神经网络（CVP-CDNN），用于求解时变复西尔维斯特方程。阐述了两种CVP-CDNN（即I型和II型CVP-CDNN），并证明其有效。如果使用线性激活函数，所提出的CVP-CDNN可以实现超指数性能。考虑了一些激活函数以寻求CVP-CDNN的更好性能，并验证了具有符号双幂激活函数的CVP-CDNN的有限时间收敛特性。具有符号双幂激活函数的CVP-CDNN的收敛时间比复固定参数收敛微分神经网络（CFP-CDNN）短。此外，通过计算机仿真比较验证了新型CVP-CDNN与传统CFP-CDNN相比具有更好的收敛性能。
