Abstract
This paper devotes to the adaptive globally synchronization within predefined-time of two time-delayed fractional-order chaotic systems. Firstly, through fractional calculus, two novel different fractional-order systems with time-delay are proposed, whose convergence is guaranteed and phase trajectory is given. Secondly, by exploiting the non-negative Lyapunov function and inequality theorem, a novel global predefined-time stability theorem is proposed, which can ensure the settling time tunable. And the upper bound of the settling time estimation is more accurate compared with the classical results. With the help of novel predefined-time stability theorem, two active controllers are designed, namely the fixed-time synchronization controller and predefined-time synchronization controller, to achieve the fixed-time synchronization and the predefined-time synchronization of two different time-delayed fractional-order chaotic systems respectively. Finally, several numerical simulations are presented in order to show the effectiveness of the proposed methods.
Highlights
The system synchronization plays a significant role in control fields and industrial applications, especially in those situations where fractional calculus are demanded, such as secure communication [1], [2], complex neural networks [3], [4] and automatic control [5], [6]
On the basis of fixed-time synchronization theory and non-negative Lyapunov function, the globally predefined-time stability theorem of fractional-order chaotic system has been proposed
For predefined-time stability, by setting the tunable parameter Tc in advance, the designed controller can achieve synchronization of drive system and corresponding response system within the upper bounded of settling time
Summary
The system synchronization plays a significant role in control fields and industrial applications, especially in those situations where fractional calculus are demanded, such as secure communication [1], [2], complex neural networks [3], [4] and automatic control [5], [6]. [26] designed an adaptive and state-feedback controller to investigate the finite-time stabilization problem of fractional-order chaotic system. [27] provided a feedback controller to analyse the finite-time synchronization of fractional-order time-delayed system. [31] designed a fractional-order terminal sliding mode control function to achieve the fractional-order chaotic system stability within fixed-time. This paper will concentrate on the adaptive predefined-time synchronization of two different fractional-order time-delayed systems. (2) A fixed-time synchronization controller is designed to enforce the drive-response system convergence within the upper bound of the settling time.
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