Finite-time synchronization of fractional-order uncertain quaternion-valued neural networks via slide mode control

Abstract

This paper investigates finite-time synchronization of fractional-order quaternion-valued neural networks (F-QV-NNs), involving uncertainties in the system parameters. We adopt a combined approach of sliding mode control (SMC) and a non-separation strategy to achieve finite-time synchronization. Based on SMC theory, we construct a specific sliding surface and design a controller to ensure the occurrence of sliding motion. To achieve the desired sliding motion, we apply the fractional Lyapunov direct method to guide the system's states to the designed sliding surface. Moreover, the derived sufficient conditions ensure finite-time synchronization within the models. Lastly, we give a numerical example to validate the effectiveness of the acquired results.

Keywords:

• Fractional derivative
• quaternion
• neural networks
• sliding mode control
• synchronization

2020 Mathematics Subject Classifications:

• 26A33
• 34D06
• 92B20

Acknowledgments

The authors would like to express their sincere thanks to the editor and anonymous reviewers for constructive comments and suggestions to improve the quality of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Md Samshad Hussain Ansari would like to express his gratitude to the Council for Scientific and Industrial Research (CSIR), India, for the Ph.D. fellowship [file number 09/1058(0026)/2021-EMR-I].