A nonlinear and noise-tolerant ZNN model solving for time-varying linear matrix equation

Xiaoxiao Li, Jiguo Yu, Shuai Li, Lina Ni

Research output: Journal article publicationJournal articleAcademic researchpeer-review

32 Citations (Scopus)


The Zhang neural network (ZNN) has attracted a great deal of interest from a large number of researchers because of its significant advantage in solving the various time-varying problems by the monotonously increasing odd activation functions. Many related models have been proposed for time-varying matrix solutions, however, provided that the noise is zero or the preprocessing of de-noising is conducted. Therefore, many of the models previously proposed are not suitable for real-world situations. In this study, a nonlinear and noise-tolerant ZNN model, named NNT-ZNN, is proposed and discussed based on the matrix-valued error function. Theoretically, we prove that the proposed NNT-ZNN model can be globally converged to the theory solution of the considered time-varying equation, regardless of any activation function being applied. In addition, we prove that the resultant NNT-ZNN model has the superior convergence performance beside the existing ZNN models, even when noise is not zero. After that, the simulative results of the resultant NNT-ZNN model are provided by using three illustrative examples to thoroughly validate the correctness of the theoretical analysis. Moreover, the simulation comparison between the proposed NNT-ZNN model and the existing ZNN-1 model is conducted, which further show that availability and excellence of the resultant NNT-ZNN model, and robustness to noise.

Original languageEnglish
Pages (from-to)70-78
Number of pages9
Publication statusPublished - 23 Nov 2018


  • Activation functions
  • Constant and time-varying noise
  • Nonlinear and noise-tolerant ZNN (NNT-ZNN)
  • Theoretical analysis

ASJC Scopus subject areas

  • Computer Science Applications
  • Cognitive Neuroscience
  • Artificial Intelligence


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