Leader-follower multi-agent flocking with bounded missing data and random communication radius

Abstract

In this paper, the leader-follower Cucker–Smale flocking system with bounded missing data and random communication radius is studied. The communication network is determined by the stochastic distance radii between agents. The process by which data are lost in the communication network is independent and identically distributed. The goal of this paper is to determine a lower bound on the probability that the agents asymptotically achieve a flocking behaviour, i.e. the relative velocities between the leader agent and other agents asymptotically vanish and the relative positions converge. Finally, a numerical simulation example is provided to illustrate the obtained results.

Keywords

Leader-follower Cucker–Smale model flocking communication radius missing data

Get full access to this article

View all access options for this article.

References

Ahn

(2010) Stochastic flocking dynamics of the Cucker–Smale model with multiplicative white noises. Journal of Mathematical Physics 51(10): 103301.

Song

You

(2016) Second-order consensus of multi-agent systems under limited interaction ranges. Automatica 68: 329–333.

Bermudez

Wicker

(2009) Connectivity of finite wireless networks with random communication range nodes. In: IEEE international conference on communications, Dresden, Germany, 14–18 June 2009, pp. 200–204. Piscataway, NJ: IEEE.

Cucker

Dong

(2009) On the critical exponent for flocks under hierarchical leadership. Mathematical Models and Methods in Applied Sciences 19(suppl 01): 1391–1404.

Cucker

Dong

(2011) A general collision-avoiding flocking framework. IEEE Transactions on Automatic Control 56(5): 1124–1129.

Cucker

Mordecki

(2008) Flocking in noisy environments. Journal de mathématiques pures et appliquées 89(3): 278–296.

Cucker

Smale

(2007) Emergent behavior in flocks. IEEE Transactions on Automatic Control 52(5): 852–862.

Dalmao

Mordecki

(2011) Cucker–Smale flocking under hierarchical leadership and random interactions. SIAM Journal on Applied Mathematics 71(4): 1307–1316.

Dalmao

Mordecki

(2012) Hierarchical Cucker–Smale model subject to random failure. IEEE Transactions on Automatic Control 57(7): 1789–1793.

10.

Dimarogonas

Kyriakopoulos

(2006) A connection between formation control and flocking behavior in nonholonomic multiagent systems. In: IEEE international conference on robotics and automation, Orlando, FL, USA, 15–19 May 2006, pp. 940–945. Piscataway, NJ: IEEE.

11.

Godsil

Royle

(2001) Algebraic Graph Theory. New York: Springer.

12.

Hatano

Mesbahi

(2005) Agreement over random networks. IEEE Transactions on Automatic Control 50(11): 1867–1872.

13.

Horn

Johnson

(1985) Matrix Analysis. New York: Cambridge University Press.

14.

Lam

Liang

(2013) Consensus control of multi-agent systems with missing data in actuators and Markovian communication failure. International Journal of Systems Science 44(10): 1867–1878.

15.

Jia

Wang

(2015) Leader-follower flocking of multiple robotic fish. IEEE/ASME Transactions on Mechatronics 20(3): 1372–1383.

16.

Leonard

Young

Hochgraf

et al . (2012) In the dance studio: analysis of human flocking. In: American control conference, Montreal, Canada, 27–29 June 2012, pp. 4333–4338. Piscataway, NJ: IEEE.

17.

Xue

(2010) Cucker–Smale flocking under rooted leadership with fixed and switching topologies. SIAM Journal on Applied Mathematics 70(8): 3156–3174.

18.

Xue

(2014) Emergent phenomena in an ensemble of Cucker–Smale particles under joint rooted leadership. Mathematical Models and Methods in Applied Sciences 24(7): 1389–1419.

19.

Austin

Chen

(2011) Flocking in multi-agent systems with active virtual leader and time-varying delays coupling. Communications in Nonlinear Science and Numerical Simulation 16(2): 1014–1026.

20.

Martin

Fazeli

Jadbabaie

et al . (2012) Multi-agent flocking with random communication radius. In: American control conference, Montreal, Canada, 27–29 June 2012, pp. 3871–3876. Piscataway, NJ: IEEE.

21.

Martin

Girard

Fazeli

et al . (2014) Multiagent flocking under general communication rule. Transactions on Control of Network Systems 1(2): 155–166.

22.

Matei

Baras

Somarakis

(2013) Convergence results for the linear consensus problem under Markovian random graphs. SIAM Journal on Control and Optimization 51(2): 1574–1591.

23.

Metropolis

Ulam

(1949) The Monte Carlo method. Journal of the American Statistical Association 44(247): 335–341.

24.

Zheng

(2015) Containment control of second-order discrete-time multi-agent systems with Markovian missing data. IET Control Theory & Applications 9(8): 1229–1237.

25.

Cheng

(2010) Leader-following consensus of multi-agent systems under fixed and switching topologies. Systems & Control Letters 59(3): 209–217.

26.

Olfati-Saber

(2006) Flocking for multi-agent dynamic systems: algorithms and theory. IEEE Transactions on Automatic Control 51(3): 401–420.

27.

Qin

Gao

(2012) A sufficient condition for convergence of sampled-data consensus for double-integrator dynamics with nonuniform and time-varying communication delays. IEEE Transactions on Automatic Control 57(9): 2417–2422.

28.

Xue

(2015) Cucker–Smale flocking with randomly failed interactions. Journal of the Franklin Institute 352(3): 1099–1118.

29.

Schenato

(2008) Optimal estimation in networked control systems subject to random delay and packet drop. IEEE Transactions on Automatic Control 53(5): 1311–1317.

30.

Shao

Qin

Bishop

et al . (2016) A novel analysis on the efficiency of hierarchy among leader-following systems. Automatica 73: 215–222.

31.

Shen

(2007) Cucker–Smale flocking under hierarchical leadership. SIAM Journal on Applied Mathematics 68(3): 694–719.

32.

Wang

Lin

(2009) Flocking for multi-agents with a virtual leader. IEEE Transactions on Automatic Control 54(2): 293–307.

33.

Tahbaz-Salehi

Jadbabaie

(2008) On consensus over random networks. IEEE Transactions on Automatic Control 53(3): 791–795.

34.

Tahbaz-Salehi

Jadbabaie

(2010) Consensus over ergodic stationary graph processes. IEEE Transactions on Automatic Control 55(1): 225–230.

35.

Tanner

Jadbabaie

Pappas

(2007) Flocking in fixed and switching networks. IEEE Transactions on Automatic Control 52(5): 863–868.

36.

Xiong

Lam

(2007) Stabilization of linear systems over networks with bounded packet loss. Automatica 43: 80–87.

37.

Zhan

(2013) Flocking of multi-agent systems via model predictive control based on position-only measurements. IEEE Transactions on Industrial Informatics 9(1): 377–385.

38.

Zhang

Fricke

Garg

(2013) Spill detection and perimeter surveillance via distributed swarming agents. IEEE/ASME Transactions on Mechatronics 18(1): 121–129.

39.

Zheng

Xie

et al . (2018) Consensusability of discrete-time multi-agent systems with communication delay and packet dropouts. IEEE Transactions on Automatic Control. Epub ahead of print 12 June 2018. DOI: 10.1109/TAC.2018.2846679.