Adaptive finite-time synchronisation of variable-order fractional chaotic systems for secure communication

Abstract

The variable-order fractional (VOF) chaotic systems offer a promising solution for applications in secure communication due to their unique properties. This paper addresses the synchronisation problem in secure communication for these systems, which have uncertainties and external disturbances with unknown bounds. According to the variable-order fractional type Mittag-Leffler stability theorem, a fractional-order derivative is applied to a sliding surface, and suitable adaptive laws are devised to address uncertainties and disturbances. A variable-order fractional control strategy and a new criterion are developed to ensure the synchronisation error systems achieve asymptotic stability in finite time, for which the upper limit can be obtained. Simulation outcomes demonstrate the efficacy of the proposed synchronisation strategy in secure communication scenarios.

Keywords:

• Chaotic systems
• finite-time stability
• variable-order fractional (VOF)
• synchronisation control
• adaptive control
• secure communication

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

Disclosure statement

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

Additional information

Funding

This research received partial support from the Zhejiang Natural Science Foundation [grant number Z23F030027], National Natural Science Foundation of China [grant number 62203041] and Fundamental Research Funds for the Central Universities [grant number 2022JBMC029].