An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation

Lei Ding; Lin Xiao; Kaiqing Zhou; Yonghong Lan; Yongsheng Zhang; Jichun Li

doi:10.1109/ACCESS.2019.2896983

An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation

Lei Ding, Lin Xiao, Kaiqing Zhou, Yonghong Lan, Yongsheng Zhang, Jichun Li

SCEDT Engineering

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Abstract

Complex-valued time-varying Sylvester equation (CVTVSE) has been successfully applied into mathematics and control domain. However, the computation load of solving CVTVSE will rise significantly with the increase of sampling rate, and it is a challenging job to tackle the CVTVSE online. In this paper, a new sign-multi-power activation function is designed. Based on this new activation function, an improved complex-valued Zhang neural network (ICZNN) model for tackling the CVTVSE is established. Furthermore, the strict proof for the maximum time of global convergence of the ICZNN is given in detail. A total of two numerical experiments are employed to verify the performance of the proposed ICZNN model, and the results show that, as compared with the previous Zhang neural network (ZNN) models with different nonlinear activation functions, this ICZNN model with the sign-multi-power activation function has a faster convergence speed to tackle the CVTVSE.

Original language	English
Article number	8632909
Pages (from-to)	19291-19302
Number of pages	12
Journal	IEEE Access
Volume	7
DOIs	https://doi.org/10.1109/ACCESS.2019.2896983
Publication status	Published - 1 Feb 2019

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10.1109/ACCESS.2019.2896983

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title = "An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation",

abstract = "Complex-valued time-varying Sylvester equation (CVTVSE) has been successfully applied into mathematics and control domain. However, the computation load of solving CVTVSE will rise significantly with the increase of sampling rate, and it is a challenging job to tackle the CVTVSE online. In this paper, a new sign-multi-power activation function is designed. Based on this new activation function, an improved complex-valued Zhang neural network (ICZNN) model for tackling the CVTVSE is established. Furthermore, the strict proof for the maximum time of global convergence of the ICZNN is given in detail. A total of two numerical experiments are employed to verify the performance of the proposed ICZNN model, and the results show that, as compared with the previous Zhang neural network (ZNN) models with different nonlinear activation functions, this ICZNN model with the sign-multi-power activation function has a faster convergence speed to tackle the CVTVSE.",

author = "Lei Ding and Lin Xiao and Kaiqing Zhou and Yonghong Lan and Yongsheng Zhang and Jichun Li",

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doi = "10.1109/ACCESS.2019.2896983",

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T1 - An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation

AU - Ding, Lei

AU - Xiao, Lin

AU - Zhou, Kaiqing

AU - Lan, Yonghong

AU - Zhang, Yongsheng

AU - Li, Jichun

PY - 2019/2/1

Y1 - 2019/2/1

N2 - Complex-valued time-varying Sylvester equation (CVTVSE) has been successfully applied into mathematics and control domain. However, the computation load of solving CVTVSE will rise significantly with the increase of sampling rate, and it is a challenging job to tackle the CVTVSE online. In this paper, a new sign-multi-power activation function is designed. Based on this new activation function, an improved complex-valued Zhang neural network (ICZNN) model for tackling the CVTVSE is established. Furthermore, the strict proof for the maximum time of global convergence of the ICZNN is given in detail. A total of two numerical experiments are employed to verify the performance of the proposed ICZNN model, and the results show that, as compared with the previous Zhang neural network (ZNN) models with different nonlinear activation functions, this ICZNN model with the sign-multi-power activation function has a faster convergence speed to tackle the CVTVSE.

AB - Complex-valued time-varying Sylvester equation (CVTVSE) has been successfully applied into mathematics and control domain. However, the computation load of solving CVTVSE will rise significantly with the increase of sampling rate, and it is a challenging job to tackle the CVTVSE online. In this paper, a new sign-multi-power activation function is designed. Based on this new activation function, an improved complex-valued Zhang neural network (ICZNN) model for tackling the CVTVSE is established. Furthermore, the strict proof for the maximum time of global convergence of the ICZNN is given in detail. A total of two numerical experiments are employed to verify the performance of the proposed ICZNN model, and the results show that, as compared with the previous Zhang neural network (ZNN) models with different nonlinear activation functions, this ICZNN model with the sign-multi-power activation function has a faster convergence speed to tackle the CVTVSE.

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An Improved Complex-Valued Recurrent Neural Network Model for Time-Varying Complex-Valued Sylvester Equation

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