Nonexistence of the Asymptotic Flocking in the Cucker-Smale Model With Short Range Communication Weights

• 成果类型: Article
• 署名作者: Yin, Xiuxia; Gao, Zhiwei; Chen, Zili; Fu, Yichuan
• 署名单位: Nanchang University; Northumbria University
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3063951
• 发表日期: 2022
• 页码: 1067-1072
• 关键词: Asymptotic flocking; communication weights; Cucker-Smale (C-S) model; multiagent system

摘要

For the long range communicated Cucker-Smale model, the asymptotic flocking exists for any initialcondition. It is noted that, for the short range communicated Cucker-Smale model, the asymptotic flocking only holds for very restricted initial conditions. In this case, the nonexistence of the asymptotic flocking has been frequently observed in numerical simulations, however, the theoretical results are far from perfect. In this note, we first point out that the nonexistence of the asymptotic flocking is equivalent to the unboundedness of the second order space moment, i.e., sup(t) Sigma vertical bar x(i) (t) - x(j) (t)vertical bar(2) = infinity. Furthermore, by taking the second derivative and then integrating, we establish a new and key equality about this moment. At last, we use this equality and relevant technical lemmas to deduce a general sufficient condition to the nonexistence of the asymptotic flocking.