Finite-time flocking of a Cucker-Smale system with external perturbation and intermittent control

Qiming Liu; Jianlong Ren; Shihua Zhang; Qiming Liu; Jianlong Ren; Shihua Zhang

doi:10.3934/math.2025292

AIMS Mathematics

2025, Volume 10, Issue 3: 6406-6428. doi: 10.3934/math.2025292

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Finite-time flocking of a Cucker-Smale system with external perturbation and intermittent control

Shijiazhuang Branch, Army Engineering University of PLA, Shijiazhuang, 050003, China

Received: 08 January 2025 Revised: 27 February 2025 Accepted: 18 March 2025 Published: 21 March 2025
MSC : 93A16, 93D40, 91D30

This study presents a modified Cucker-Smale system with external perturbation and intermittent control. First, a new finite-time stability lemma is developed, in which the settling time is determined only by the control interval's duration. Second, by imposing an assumption on external perturbation, the system can achieve collision-avoidance flocking. Third, finite-time flocking is achieved without the sign function, which effectively avoids the undesirable chattering phenomenon in the system. Finally, numerical simulations validate the theoretical analysis, and parameter sensitivity analysis offers important guidance for practical applications such as unmanned aerial vehicle (UAV) formations.
- Cucker-Smale system,
- finite-time flocking,
- collision avoidance,
- external perturbation,
- intermittent control
Citation: Qiming Liu, Jianlong Ren, Shihua Zhang. Finite-time flocking of a Cucker-Smale system with external perturbation and intermittent control[J]. AIMS Mathematics, 2025, 10(3): 6406-6428. doi: 10.3934/math.2025292

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Abstract

This study presents a modified Cucker-Smale system with external perturbation and intermittent control. First, a new finite-time stability lemma is developed, in which the settling time is determined only by the control interval's duration. Second, by imposing an assumption on external perturbation, the system can achieve collision-avoidance flocking. Third, finite-time flocking is achieved without the sign function, which effectively avoids the undesirable chattering phenomenon in the system. Finally, numerical simulations validate the theoretical analysis, and parameter sensitivity analysis offers important guidance for practical applications such as unmanned aerial vehicle (UAV) formations.

References

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