Letters: Zhang neural network versus gradient-based neural network for time-varying linear matrix equation solving

Authors:
Dongsheng Guo;Chenfu Yi;Yunong Zhang
Affiliations:
School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China;School of Information Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China;School of Information Science and Technology, Sun Yat-sen University, Guangzhou 510006, China
Venue:
Neurocomputing
Year:
2011

Citing 14
Cited 1

Topics in matrix analysis

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Abstract

A type of recurrent neural networks called Zhang neural network (ZNN) is presented and investigated to provide an online solution to the time-varying linear matrix equation, A(t)X(t)B(t)+X(t)=C(t) by using a novel design method. In contrast to the gradient-based neural network (GNN), the novel design of ZNN is based on a matrix-valued indefinite error function, instead of a scalar-valued norm-based energy function. Therefore, a ZNN model depicted in implicit dynamics can globally and exponentially converge to the time-varying theoretical solution of the given linear matrix equation. Computer simulation results further demonstrate the superior performance of the ZNN model in solving the time-varying linear matrix equation compared with the conventional GNN model.