Finite-time synchronization of fractional-order heterogeneous dynamical networks with impulsive interference via aperiodical intermittent control

Tao Xie; Xing Xiong; Tao Xie; Xing Xiong

doi:10.3934/math.2025287

AIMS Mathematics

2025, Volume 10, Issue 3: 6291-6317. doi: 10.3934/math.2025287

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Research article

Finite-time synchronization of fractional-order heterogeneous dynamical networks with impulsive interference via aperiodical intermittent control

Tao Xie ^,,
Xing Xiong

School of Mathematics and Statistics, Hubei Normal University, Huangshi, 435002, China

Received: 10 December 2024 Revised: 18 February 2025 Accepted: 27 February 2025 Published: 20 March 2025
MSC : 93B35, 93D23

This paper addresses the problem of ensuring finite-time synchronization for fractional-order heterogeneous dynamical networks via aperiodic intermittent control, where uncertain impulsive disturbances are introduced at the instants triggered by the control actions applied to the system. Under aperiodic time-triggered and event-triggered intermittent control, a Lyapunov function iteration method, based on the traditional Lyapunov method, was developed to analyze the criteria for finite-time synchronization. Several sufficient conditions were proposed to ensure finite-time synchronization. First, within the framework of finite-time and time-triggered control, the relationship between the control period width, impulsive disturbances, and configuration control parameters was established to guarantee finite-time synchronization. Second, an event-triggered mechanism was introduced into the intermittent control, where the sequence of impulsive disturbance instants was determined by a pre-designed trigger threshold. The relationship between impulsive disturbances, the event-triggered threshold, and the control period width was established. These two relationships can potentially increase the flexibility of the designed control periods and control width. Moreover, the Zeno phenomenon can be eliminated in the event-triggered mechanism. Finally, two simulations were presented to illustrate the feasibility and effectiveness of the theoretical results.
- fractional-order heterogeneous dynamical networks,
- impulsive,
- finite-time synchronization,
- aperiodic intermittent control,
- event-triggered mechanism
Citation: Tao Xie, Xing Xiong. Finite-time synchronization of fractional-order heterogeneous dynamical networks with impulsive interference via aperiodical intermittent control[J]. AIMS Mathematics, 2025, 10(3): 6291-6317. doi: 10.3934/math.2025287

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Abstract

This paper addresses the problem of ensuring finite-time synchronization for fractional-order heterogeneous dynamical networks via aperiodic intermittent control, where uncertain impulsive disturbances are introduced at the instants triggered by the control actions applied to the system. Under aperiodic time-triggered and event-triggered intermittent control, a Lyapunov function iteration method, based on the traditional Lyapunov method, was developed to analyze the criteria for finite-time synchronization. Several sufficient conditions were proposed to ensure finite-time synchronization. First, within the framework of finite-time and time-triggered control, the relationship between the control period width, impulsive disturbances, and configuration control parameters was established to guarantee finite-time synchronization. Second, an event-triggered mechanism was introduced into the intermittent control, where the sequence of impulsive disturbance instants was determined by a pre-designed trigger threshold. The relationship between impulsive disturbances, the event-triggered threshold, and the control period width was established. These two relationships can potentially increase the flexibility of the designed control periods and control width. Moreover, the Zeno phenomenon can be eliminated in the event-triggered mechanism. Finally, two simulations were presented to illustrate the feasibility and effectiveness of the theoretical results.

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