Finite-time synchronization of fractional order neural networks via sampled data control with time delay

Volume 35, Issue 4, pp 374--387 https://dx.doi.org/10.22436/jmcs.035.04.01

Publication Date: May 31, 2024 Submission Date: March 15, 2024 Revision Date: April 12, 2024 Accteptance Date: April 21, 2024

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Authors

S. Jose - School of Advanced Sciences, Vellore Institute of Technology, Chennai, India. V. Parthiban - School of Advanced Sciences, Vellore Institute of Technology, Chennai, India.

Abstract

This paper investigates the problem of finite-time synchronization (FTS) of fractional-order neural networks (FONNs) with time-delay via sampled data control (SDC) scheme. To achieve FTS criteria, a sampled-data control (SDC) scheme is implemented in the slave model of FONNs. And, this investigation is based on the solution of the time-delayed NNs by using Laplace transform, Mittag-Leffler function (MLF), and the generalized Grownwall inequality. Furthermore, under the proposed SDC scheme, the FTS conditions are derived for two cases of fractional order \(\alpha\), such as \(0<\alpha<1\) and \(1<\alpha<2\). The derived conditions ensure that the slave FONNs is asymptotically synchronized with master FONNs. Finally, two numerical examples are given to show the effectiveness of derived FTS criteria, for fractional order lying between \(0<\alpha<1\) and \(1<\alpha<2\).

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Keywords

• Fractional-order derivative
• neural networks
• finite-time synchronization
• time-delay
• Mittag-leffler function

MSC

•  34A08
•  68T07
•  34D06

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