Cucker-Smale flocking subject to random failure on general digraphs

Abstract This paper studies the Cucker–Smale (C–S) flocking subject to random failure under general interaction topologies, which contain the hierarchical leadership and rooted leadership as special cases. Furthermore, at each time step, each of the agents can fail to interact with any of its neighbors. The random failures are assumed to be not independent. We prove that the flocking would occur almost surely under some conditions on the initial state of the flock only. The result suggests that the C–S flocking system on general digraphs can endure random failure in interactions. Finally, several numerical simulations are provided to illustrate the obtained results.

[1]  Felipe Cucker,et al.  A General Collision-Avoiding Flocking Framework , 2011, IEEE Transactions on Automatic Control.

[2]  A. Czirók,et al.  Collective Motion , 1999, physics/9902023.

[3]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[4]  Jesús Rosado,et al.  Asymptotic Flocking Dynamics for the Kinetic Cucker-Smale Model , 2010, SIAM J. Math. Anal..

[5]  Roland Bouffanais,et al.  Resilience and Controllability of Dynamic Collective Behaviors , 2013, PloS one.

[6]  F. Cucker,et al.  Flocking in noisy environments , 2007, 0706.3343.

[7]  Xiaoping Xue,et al.  Cucker--Smale Flocking under Rooted Leadership with Fixed and Switching Topologies , 2010, SIAM J. Appl. Math..

[8]  Antoine Girard,et al.  Multiagent Flocking Under General Communication Rule , 2014, IEEE Transactions on Control of Network Systems.

[9]  I. Couzin,et al.  Effective leadership and decision-making in animal groups on the move , 2005, Nature.

[10]  Warren E. Dixon,et al.  Leader-follower containment control over directed random graphs , 2016, Autom..

[11]  Seung-Yeal Ha,et al.  Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system , 2009 .

[12]  Ernesto Mordecki,et al.  Cucker-Smale Flocking Under Hierarchical Leadership and Random Interactions , 2009, SIAM J. Appl. Math..

[13]  Li Qiu,et al.  Flocking of the Cucker-Smale Model on General Digraphs , 2017, IEEE Transactions on Automatic Control.

[14]  Tam'as Vicsek,et al.  Patterns, transitions and the role of leaders in the collective dynamics of a simple robotic flock , 2011 .

[15]  Ernesto Mordecki,et al.  Hierarchical Cucker-Smale Model Subject to Random Failure , 2012, IEEE Transactions on Automatic Control.

[16]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[17]  Felipe Cucker,et al.  ON THE CRITICAL EXPONENT FOR FLOCKS UNDER HIERARCHICAL LEADERSHIP , 2009 .

[18]  Lining Ru,et al.  Cucker-Smale flocking with randomly failed interactions , 2015, J. Frankl. Inst..

[19]  T. Vicsek,et al.  Hierarchical group dynamics in pigeon flocks , 2010, Nature.

[20]  Felipe Cucker,et al.  Emergent Behavior in Flocks , 2007, IEEE Transactions on Automatic Control.

[21]  Pedro Elosegui,et al.  Extension of the Cucker-Smale Control Law to Space Flight Formations , 2009 .

[22]  Seung-Yeal Ha,et al.  A simple proof of the Cucker-Smale flocking dynamics and mean-field limit , 2009 .

[23]  Jianhong Shen,et al.  Cucker–Smale Flocking under Hierarchical Leadership , 2006, q-bio/0610048.

[24]  Xiaowu Mu,et al.  Hierarchical Cucker-Smale flocking under random interactions with time-varying failure probabilities , 2018, J. Frankl. Inst..