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Higher-Order ZNN Dynamics

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Abstract

Several improvements of the Zhang neural network (ZNN) dynamics for solving the time-varying matrix inversion problem are presented. Introduced ZNN dynamical design is termed as ZNN models of the order p, \(p\ge 2\), and it is based on the analogy between the proposed continuous-time dynamical systems and underlying discrete-time pth order hyperpower iterative methods for computing the constant matrix inverse. Such ZNN design is denoted by \(\hbox {ZNN}_H^p\). Particularly, the \(\hbox {ZNN}_H^2\) design coincides with the standard ZNN design. Moreover, \(\hbox {ZNN}_H^3\) design represents a time-varying generalization of the previously defined ZNNCM model. In addition, an integration-enhanced noise-handling \(\hbox {ZNN}_H^p\) model, termed as \(\hbox {IENHZNN}_H^p\), is introduced. In the time-invariant case, we present a hybrid enhancement of the \(\hbox {ZNN}_H^p\) model, shortly termed as \(\hbox {HZNN}_H^p\), and investigate it theoretically and numerically. Theoretical and numerical comparisons between the improved and standard ZNN dynamics are considered.

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Authors and Affiliations

  1. Faculty of Sciences and Mathematics, University of Niš, Višegradska 33, Niš, 18000, Serbia

    Predrag S. Stanimirović

  2. Division of Mathematics and Informatics, Department of Economics, National and Kapodistrian University of Athens, Sofokleous 1 Street, 10559, Athens, Greece

    Vasilios N. Katsikis

  3. College of Engineering, Swansea University, Swansea, SA1 7EN, UK

    Shuai Li

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  1. Predrag S. Stanimirović
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  2. Vasilios N. Katsikis
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  3. Shuai Li
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Correspondence to Predrag S. Stanimirović.

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Predrag S. Stanimirović gratefully acknowledge support from the Ministry of Education and Science, Republic of Serbia, Grant No. 174013, and from the bilateral project between China and Serbia “The theory of tensors, operator matrices and applications (No. 4-5)”.

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Stanimirović, P.S., Katsikis, V.N. & Li, S. Higher-Order ZNN Dynamics. Neural Process Lett 51, 697–721 (2020). https://doi.org/10.1007/s11063-019-10107-8

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  • DOI: https://doi.org/10.1007/s11063-019-10107-8

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