A New Varying-Parameter Recurrent Neural-Network for Online Solution of Time-Varying Sylvester Equation

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...

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Bibliographic Details
Published in:IEEE transactions on cybernetics 2018-11, Vol.48 (11), p.3135-3148
Main Authors: Zhang, Zhijun, Zheng, Lunan, Weng, Jian, Mao, Yijun, Lu, Wei, Xiao, Lin
Format: Article
Language:English
Subjects:
Biological neural networks
Computer simulation
Computer simulations
Control theory
Convergence
convergence and robustness
Mathematical analysis
Mathematical model
Neural networks
Parameters
Recurrent neural networks
Robustness
Robustness (mathematics)
time-varying equation solving
Time-varying systems
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Summary: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.
ISSN:2168-2267
2168-2275
DOI:10.1109/TCYB.2017.2760883