| Citation: |
Jianlong Ren, Qiming Liu, Jiangyan He. THE COLLISION-AVOIDING FINITE-TIME FLOCKING OF A CUCKER-SMALE MODEL WITH PINNING CONTROL AND EXTERNAL PERTURBATION[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1503-1519. doi: 10.11948/20240273
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THE COLLISION-AVOIDING FINITE-TIME FLOCKING OF A CUCKER-SMALE MODEL WITH PINNING CONTROL AND EXTERNAL PERTURBATION
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Abstract
The Cucker-Smale model plays a vital role in analyzing flocking behavior. To investigate the impact of pinning control and external perturbation on finite-time flocking behavior, a modified Cucker-Smale model that incorporates these factors is proposed in this paper. Initially, by imposing appropriate restrictions on external perturbation, the system can achieve finite-time flocking, and the upper bound of settling time is derived explicitly. Subsequently, a new sufficient condition is given to ensure collision-avoiding during the flocking process. The results show that the convergence time depends on control parameters and the convergence speed of the perturbation. Lastly, numerical simulations are provided to illustrate the derived results.
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References
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Jianlong Ren, Qiming Liu, Jiangyan He. THE COLLISION-AVOIDING FINITE-TIME FLOCKING OF A CUCKER-SMALE MODEL WITH PINNING CONTROL AND EXTERNAL PERTURBATION[J]. Journal of Applied Analysis & Computation, 2025, 15(3): 1503-1519. doi: 10.11948/20240273
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Figure 1.
The flocking without external perturbation.
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Figure 2.
The flocking with the first type of external perturbation.
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Figure 3.
The flocking with the second type of external perturbation.
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Figure 4.
The eigenvalue
$ \lambda_1 $ $ l_0 $ $ \beta $ -
Figure 5.
The flocking for different control gain
$ \beta $ -
Figure 6.
The flocking with different
$ l_0 $ -
Figure 7.
The flocking with different
$ N $