This paper considers flocking to the virtual leader in network of agents with double-integrator. A locally linear algorithm is employed which guarantees exponential flocking to the virtual leader. A lower bound for flocking rate is calculated which is independent of the initial conditions. Simulations are provided to validate the result and it is shown that the calculated rate is not over bound the actual convergence rate. The effect of coefficients of algorithm is investigated and it is shown that the similar results can be inferred from the calculated formula for the convergence rate.

References

References
1.
Reynolds
,
C. W.
,
1987
, “
Flock, Herds and Schools: A Distributed Behavioral Model
,”
Comput. Graph.
,
21
(
4
), pp.
25
34
.10.1145/37402.37406
2.
Vicsek
,
T.
,
Czirok
,
A.
,
Ben-Jacob
,
E.
,
Cohen
,
I.
, and
Shochet
,
O.
,
1995
, “
Novel Type of Phase Transition in a System of Self Driven Particles
,”
Phys. Rev. Lett.
,
75
(
6
), pp.
1226
1229
.10.1103/PhysRevLett.75.1226
3.
Jadbabaie
,
A.
,
Lin
,
J.
, and
Morse
,
S.
,
2003
, “
Coordination of Groups of Mobile Autonomous Agents Using Nearest Neighbor Rules
,”
IEEE Trans. Autom. Control
,
48
(
6
), pp.
988
1001
.10.1109/TAC.2003.812781
4.
Olfati-Saber
R.
, and
Murray
,
R.
,
2004
, “
Consensus Problems in Networks of Agents With Switching Topology and Time Delays
,”
IEEE Trans. Autom. Control
,
49
(
9
), pp.
1520
1533
.10.1109/TAC.2004.834113
5.
Olshevsky
,
A.
, and
Tsitsiklis
,
J. N.
,
2006
, “
Convergence Rates in Distributed Consensus and Averaging
,” Proceeding of the 45th
IEEE
Conference on Decision and Control
, San Diego, CA, Dec. 13–15, pp.
3387
3392
.10.1109/CDC.2006.376899
6.
Bliman
,
P.-A.
,
Nedic
,
A.
, and
Ozdaglar
,
A.
,
2008
, “
Rate of Convergence for Consensus With Delays
,” Proceeding of the 47th
IEEE
Conference on Decision and Control
,
Cancun
,
Mexico
, Dec. 9–11, pp.
4849
4854
.10.1109/CDC.2008.4738941
7.
Nedic
,
A.
, and
Ozdaglar
,
A.
,
2010
, “
Convergence Rate for Consensus With Delays
,”
J. Global Optim.
,
47
(
3
), pp.
437
456
.10.1007/s10898-008-9370-2
8.
Cao
,
M.
,
Morse
,
A. S.
, and
Anderson
,
B. D. O.
,
2008
, “
Reaching a Consensus in a Dynamically Changing Environment: Convergence Rates, Measurement Delays and Asynchronous Events
,”
SIAM J. Control Optim.
,
47
(
2
), pp.
601
623
.10.1137/060657029
9.
Cao
,
M.
,
Spielman
,
D. A.
, and
Morse
,
A. S.
,
2005
, “
A Lower Bound on Convergence of a Distributed Network Consensus Algorithm
,” Proceeding of the 44th
IEEE
Conference on Decision and Control and the European Control Conference
, Seville, Spain, Dec. 12–15, pp.
2356
2361
.10.1109/CDC.2005.1582514
10.
Ren
,
W.
,
Moore
,
K.
, and
Chen
,
Y. Q.
,
2007
, “
High-Order and Model Reference Consensus Algorithms in Cooperative Control of Multivehicle Systems
,”
ASME J. Dyn. Sys., Meas., Control
,
129
(
5
), pp.
678
688
.10.1115/1.2764508
11.
Wieland
,
P.
,
Kim
,
J. S.
,
Scheu
,
H.
, and
Allgower
,
F.
,
2008
, “
On Consensus in Multi-Agent Systems With Linear High-Order Agents
,”
Proceeding of the 17th
IFAC
, Seoul, Korea, July 6–11, pp.
1541
1546
.10.3182/20080706-5-KR-1001.00263
12.
Tanner
,
H. G.
,
Jadbabaie
,
A.
, and
Pappas
,
G. J.
,
2003
, “
Stable Flocking of Mobile Agents, Part I: Fixed Topology
,” Proceeding of the 42nd
IEEE
Conference on Decision and Control
, San Diego, CA, Dec. 9–12, pp.
2010
2015
.10.1109/CDC.2003.1272910
13.
Tanner
,
H. G.
,
Jadbabaie
,
A.
, and
Pappas
,
G. J.
,
2003
, “
Stable Flocking of Mobile Agents, Part II: Dynamic Topology
,” Proceeding of the 42nd
IEEE
Conference on Decision and Control
, San Diego, CA, Dec. 9–12, pp.
2016
2021
.10.1109/CDC.2003.1272911
14.
Xie
,
G.
, and
Wang
,
L.
,
2007
, “
Consensus Control for a Class of Networks of Dynamic Agents
,”
Int. J. Robust Nonlinear Control
,
17
(
10–11
), pp.
941
959
.10.1002/rnc.1144
15.
Shi
,
H.
,
Wang
,
L.
, and
Chu
,
T.
,
2005
, “
Virtual Leader Approach to Coordinated Control of Multiple Mobile Agents With Asymmetric Interactions
,” Proceedings of the 44th
IEEE
Conference on Decision and Control and the European Control Conference
, Seville, Spain, Dec. 12–15, pp.
6250
6255
.10.1109/CDC.2005.1583163
16.
Olfati-Saber
,
R.
,
2006
, “
Flocking for Multi Agent Dynamic Systems: Algorithms and Theory
,”
IEEE Trans. Autom. Control
,
51
(
3
), pp.
988
1001
.10.1109/TAC.2005.864190
17.
Porfiri
,
M.
,
Roberson
,
D. G.
, and
Stilwell
,
D. J.
,
2007
, “
Tracking and Formation Control of Multiple Autonomous Agents: A Two-Level Consensus Approach
,”
Automatica
,
43
(
8
), pp.
1318
1328
.10.1016/j.automatica.2007.01.004
18.
Peng
,
L.
,
Yingmin
,
J.
,
Junping
,
D.
, and
Shiying
,
Y.
,
2007
, “
Distributed Consensus Control for Second-Order Agents With Fixed Topology and Time-Delay
,”
Proceedings of 26th Chinese Control Conference
(
CCC
),
Zhangjiajie
, Hunan, China, July 26–31, pp.
577
581
.10.1109/CHICC.2006.4347165
19.
Zhu
,
J.
,
Tian
,
Y. P.
, and
Kuang
,
J.
,
2009
, “
On the General Consensus Protocol of Multi-Agent Systems With Double-Integrator Dynamics
,”
Linear Algebra Appl. J.
,
431
(
5-7
), pp.
701
715
.10.1016/j.laa.2009.03.019
20.
Khalil
,
H. K.
,
2002
,
Nonlinear Systems
,
3rd ed.
,
Prentice-Hall
,
Englewood Cliffs, NJ
.
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