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Flocking of Multi-particle Swarm with Group Coupling Structure and Measurement Delay
  
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KeyWord:Time-asymptotic flocking; Group coupling; Intra-group and inter-group interaction; Measurement delay
Author NameAffiliation
Maoli Chen College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, Hunan 410073, China 
Yicheng Liu College of Liberal Arts and Sciences, National University of Defense Technology, Changsha, Hunan 410073, China 
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Abstract:
      We investigate the flocking conditions of a group coupling system with time delays, in which the communication between particles includes inter-group and intra-group interactions, and the time delay comes from the theory of moving object observation. As an effective model, we introduce a system of nonlinear functional differential equations to describe its dynamic evolution mechanism. By constructing two differential inequalities on velocity and velocity fluctuation from a continuity argument, and using the Lyapunov functional approach, we present some sufficient conditions for the existence of asymptotic flocking solutions to the coupling system, in which an upper bound of the delay allowed by the system is quantitatively given to ensure the emergence of flocking behavior. All results are novel and can be illustrated by using some specific numerical simulations.