Discrete-time Zhang neural network and numerical algorithm for time-varying linear equations solving

Since 2001, a special class of recurrent neural network (RNN), termed Zhang neural network (ZNN), has been proposed, generalized and exploited for online solution of time-varying problems by following Zhang et al's design method. In this paper, for possible digital hardware realization, discrete-time ZNN models are proposed and investigated for time-varying linear equations solving. Such discrete-time ZNN models make use of time-derivative information of the time-varying coefficients. For comparison purposes, a discrete-time gradient-based neural network (GNN) model is also presented to solve the same problem. Simulative and numerical results illustrate the efficacy and superiority of these discrete-time ZNN models used for time-varying linear equations solving, as compared to the GNN model.

[1]  Shuzhi Sam Ge,et al.  Design and analysis of a general recurrent neural network model for time-varying matrix inversion , 2005, IEEE Transactions on Neural Networks.

[2]  Jos,et al.  Convergence Analysis of a Discrete-Time Recurrent Neural Network to Perform Quadratic Real Optimization with Bound Constraints , 1998 .

[3]  Michael A. Arbib,et al.  The handbook of brain theory and neural networks , 1995, A Bradford book.

[4]  María José Pérez-Ilzarbe.  Convergence analysis of a discrete-time recurrent neural network to perform quadratic real optimization with bound constraints , 1998, IEEE Trans. Neural Networks.

[5]  Yunong Zhang,et al.  Analogue recurrent neural network for linear algebraic equation solving , 2008 .

[6]  Yunong Zhang,et al.  Comparison on Zhang neural network and gradient neural network for time-varying linear matrix equation AXB = C solving , 2008, 2008 IEEE International Conference on Industrial Technology.

[7]  Albert D. Carlson,et al.  The Handbook of Brain Theory and Neural Networks.Second Edition. Edited byMichael A Arbib.A Bradford Book. Cambridge (Massachusetts): MIT Press. $165.00. xvii + 1290 p; ill.; index. ISBN: 0–262–01197–2. 2003. , 2003 .

[8]  Honggeng Yang,et al.  Dynamic reactive power optimization using mathematical morphology and genetic algorithm , 2008, 2008 IEEE International Conference on Industrial Technology.

[9]  Jun Wang,et al.  A recurrent neural network for solving Sylvester equation with time-varying coefficients , 2002, IEEE Trans. Neural Networks.

[10]  Ke Chen,et al.  Performance Analysis of Gradient Neural Network Exploited for Online Time-Varying Matrix Inversion , 2009, IEEE Transactions on Automatic Control.

[11]  George Lindfield,et al.  Numerical Methods Using MATLAB , 1998 .