CSIAM Trans. Appl. Math., 5 (2024), pp. 73-109.
Published online: 2024-02
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Body attitude coordination plays an important role in multi-airplane synchronization. In this paper, we study the flocking dynamics of a modified model for body attitude coordination. In contrast to the original body attitude alignment models in Degond et al. (Math. Models Methods Appl. Sci., 27(6): 1005–1049, 2017) and Ha et al. (Discrete Contin. Dyn. Syst., 40(4): 2037–2060, 2020), we introduce the velocity alignment term and assume the velocity of each agent is variable. More precisely, the adjoint coefficient will vary with the linked individual changes. In this case, synchronization would include the body attitude alignment and velocity alignment. It will generate a new collective behaviour which is called body attitude flocking. As results, we present two sufficient frameworks leading to the body attitude flocking by technique estimates. Also, we show the finite-in-time stability of the system which is valid on any finite time interval. In addition, we formally derive a kinetic model of the model for body attitude coordination using the BBGKY hierarchy. We prove the well-posedness of the kinetic equation and show a rigorous justification for the mean-field limit of our model. Moreover, we present a sufficient condition for asymptotic flocking in the kinetic model. Finally, we also give the numerical simulations to verify our analysis results.
}, issn = {2708-0579}, doi = {https://doi.org/10.4208/csiam-am.SO-2023-0013}, url = {http://global-sci.org/intro/article_detail/csiam-am/22921.html} }Body attitude coordination plays an important role in multi-airplane synchronization. In this paper, we study the flocking dynamics of a modified model for body attitude coordination. In contrast to the original body attitude alignment models in Degond et al. (Math. Models Methods Appl. Sci., 27(6): 1005–1049, 2017) and Ha et al. (Discrete Contin. Dyn. Syst., 40(4): 2037–2060, 2020), we introduce the velocity alignment term and assume the velocity of each agent is variable. More precisely, the adjoint coefficient will vary with the linked individual changes. In this case, synchronization would include the body attitude alignment and velocity alignment. It will generate a new collective behaviour which is called body attitude flocking. As results, we present two sufficient frameworks leading to the body attitude flocking by technique estimates. Also, we show the finite-in-time stability of the system which is valid on any finite time interval. In addition, we formally derive a kinetic model of the model for body attitude coordination using the BBGKY hierarchy. We prove the well-posedness of the kinetic equation and show a rigorous justification for the mean-field limit of our model. Moreover, we present a sufficient condition for asymptotic flocking in the kinetic model. Finally, we also give the numerical simulations to verify our analysis results.