On Collision Avoiding Fixed-Time Flocking with Measurable Diameter to a Cucker–Smale-Type Self-Propelled Particle Model

Dealing with the fixed-time flocking issue is one of the most challenging problems for a Cucker–Smale-type self-propelled particle model. In this article, the fixed-time flocking is established by employing a fixed-time stability theorem when the communication weight function has a positive infimum....

Full description

Saved in:
Bibliographic Details
Published inComplexity (New York, N.Y.) Vol. 2020; no. 2020; pp. 1 - 12
Main Authors Ouyang, Zigen, Xu, Zhenghua, Liu, Hongliang, Xiao, Qizhen
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 2020
Hindawi
John Wiley & Sons, Inc
Hindawi Limited
Hindawi-Wiley
Subjects
Animal behavior
Birds
Collision avoidance
Communication
Comparative analysis
Design parameters
Diameters
Inequality
Infimum
Stability
Upper bounds
Weighting functions
Iran
Online AccessGet full text

Cover

More Information
Summary:Dealing with the fixed-time flocking issue is one of the most challenging problems for a Cucker–Smale-type self-propelled particle model. In this article, the fixed-time flocking is established by employing a fixed-time stability theorem when the communication weight function has a positive infimum. Compared with the initial condition-based finite-time stability, an upper bound of the settling time in this paper is merely dependent on the design parameters. Moreover, the size of the final flocking can be estimated by the number of particles and the initial states of the system. In addition, a sufficient condition is formulated to guarantee that all particles do not collide during the process of the flocking. These results can give a reasonable explanation to some flocking phenomena such as bird flocks, fish schools, or human group behaviors. Finally, three numerical examples are granted to display the performance of the obtained results.
ISSN:1076-2787
1099-0526
DOI:10.1155/2020/1094950