Simulink Modeling and Comparison of Zhang Neural Networks and Gradient Neural Networks for Time-Varying Lyapunov Equation Solving

2008 ◽  
Author(s):  
Yunong Zhang ◽  
Ke Chen ◽  
Xuezhong Li ◽  
Chengfu Yi ◽  
Hong Zhu
Keyword(s):  
Neural Networks ◽  
Lyapunov Equation ◽  
Time Varying ◽  
Equation Solving ◽  
Zhang Neural Networks

scholarly journals Noise-tolerant continuous-time Zhang neural networks for time-varying Sylvester tensor equations

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Sun Min ◽  
Liu Jing
Keyword(s):  
Neural Networks ◽  
Continuous Time ◽  
Time Derivative ◽  
Time Varying ◽  
Gradient Based ◽  
Noise Tolerant ◽  
Derivative Information ◽  
Residual Errors ◽  
Theoretical Analyses ◽  
Zhang Neural Networks

Abstract In this paper, to solve the time-varying Sylvester tensor equations (TVSTEs) with noise, we will design three noise-tolerant continuous-time Zhang neural networks (NTCTZNNs), termed NTCTZNN1, NTCTZNN2, NTCTZNN3, respectively. The most important characteristic of these neural networks is that they make full use of the time-derivative information of the TVSTEs’ coefficients. Theoretical analyses show that no matter how large the unknown noise is, the residual error generated by NTCTZNN2 converges globally to zero. Meanwhile, as long as the design parameter is large enough, the residual errors generated by NTCTZNN1 and NTCTZNN3 can be arbitrarily small. For comparison, the gradient-based neural network (GNN) is also presented and analyzed to solve TVSTEs. Numerical examples and results demonstrate the efficacy and superiority of the proposed neural networks.

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