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This study revisits the sampled-data consensus algorithm for agents modelled by double-integrator dynamics under both fixed and dynamic network topology. Totally different methods are employed to perform the convergence analysis. Under certain assumptions on the sampling period and the velocity damping gain, a necessary and sufficient condition is given for the agents under fixed network topology to reach consensus. In addition, the method employed in performing the convergence analysis for the fixed case can be further extended to achieve a similar result as that in the existing literature for the dynamical case in a more general setting. The consensus equilibria are also analysed for the system evolving under a special class of dynamic network topology.
References
-
-
1)
-
Y. Wang ,
Z. Wang ,
J. Liang
.
A delay fractioning approach to global synchronization of delayed complex networks with stochastic disturbances.
Phys. Lett. A
,
39 ,
6066 -
6073
-
2)
-
P. Shi ,
S.K. Nguang
.
H∞ output feedback control of fuzzy system models under sampled measurements.
Comput. Math. Appl.
,
705 -
717
-
3)
-
H. Minc
.
(1988)
Nonnegative matrices.
-
4)
-
Z. Ji ,
Z. Wang ,
H. Lin ,
Z. Wang
.
Interconnection topologies for multi-agent coordination under leader-follower framework.
Automatica
,
12 ,
2857 -
2863
-
5)
-
Casbeer, D.W., Beard, R., Swindlehurst, A.L.: `Discrete double integrator consensus', Proc. IEEE Conf. on Decision and Control, December 2008, Cancun, Mexico, p. 2264–2269.
-
6)
-
W. Ren ,
R.W. Beard
.
Consensus seeking in multiagent systems under dynamically changing interaction topologies.
IEEE Trans. Autom. Control
,
5 ,
655 -
661
-
7)
-
Qin, J., Gao, H., Zheng, W.X.: `Sampled-data consensus for multiple agents with discrete second-order dynamics', Proc. 49th IEEE Conf. Decision Control, December 2010, Shanghai, Atlanta, GA, USA, p. 1391–1396.
-
8)
-
G. Xie ,
L. Wang
.
Consensus control for a class of networks of dynamic agents.
Int. J. Robust Nonlinear Control
,
941 -
959
-
9)
-
J.A. Fax ,
R.M. Murray
.
Information flow and cooperative control of vehicle formations.
IEEE Trans. Autom. Control
,
9 ,
1465 -
1476
-
10)
-
Hayakawa, T., Matsuzawa, T., Hara, S.: `Formation control of multi-agent systems with sampled information', Proc. IEEE Conf. on Decision and Control, December 2006, San Diego, CA, p. 4333–4338.
-
11)
-
Z. Wang ,
B. Huang ,
P. Huo
.
Sampled-data filtering with error covariance assignment.
IEEE Trans. Signal Process.
,
3 ,
666 -
670
-
12)
-
Z. Ji ,
Z. Wang ,
H. Lin ,
Z. Wang
.
Controllability of multi-agent systems with time-delay in state and switching topology.
Int. J. Control
,
2 ,
371 -
386
-
13)
-
P. Shi
.
Filtering on sampled-data systems with parametric uncertainty.
IEEE Trans. Autom. Control
,
7 ,
1022 -
1027
-
14)
-
P. Lin ,
Y. Jia
.
Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies.
Automatica
,
2154 -
2158
-
15)
-
R. Olfati-Saber ,
R.M. Murray
.
Consensus problems in networks of agents with switching topology and time-delays.
IEEE Trans. Autom. Control
,
9 ,
1520 -
1533
-
16)
-
W. Ren ,
R.W. Beard
.
(2008)
Distributed consensus in multi-vehicle cooperative control.
-
17)
-
Mohanarajah, G., Hayakawa, T.: `Influence of stochastic communication loss on the stability of a formation of multiple agents', Proc. American Control Conf., July 2007, New York, p. 341–346.
-
18)
-
N. Biggs
.
(1993)
Algebraic graph theory.
-
19)
-
Y. Cao ,
W. Ren
.
Multi-vehicle coordination for double-integrator dynamics under fixed undirected/directed interaction in a sampled-data setting.
Int. J. Robust Nonlinear Control
,
9 ,
987 -
1000
-
20)
-
H.G. Tanner ,
A. Jadbabaie ,
G.J. Pappas
.
Flocking in fixed and switching networks.
IEEE Trans. Autom. Control
,
5 ,
863 -
868
-
21)
-
Cao, Y., Ren, W.: `Sampled-data formation control under dynamic directed interaction', Proc. American Control Conf., June 2009, St. Louis, MO, p. 5186–5191.
-
22)
-
F. Xiao ,
L. Wang
.
Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays.
IEEE Trans. Autom. Control
,
8 ,
1804 -
1816
-
23)
-
J. Wolfowitz
.
Products of indecomposable, aperiodic, stochastic matrices.
Proc. Am. Math. Soc.
,
5 ,
733 -
737
-
24)
-
W. Ren ,
E. Atkins
.
Distributed multi-vehicle coordinated control via local information exchange.
Int. J. Robust Nonlinear Control
,
1002 -
1033
-
25)
-
Z. Wang ,
Y. Wang ,
Y. Liu
.
Global synchronization for discrete-time stochastic complex networks with randomly occurred nonlinearities and mixed time-delays.
IEEE Trans. Neural Netw.
,
1 ,
11 -
25
-
26)
-
W. Ren
.
Consensus strategies for cooperative control of vehicle formations.
IET Control Theory Appl.
,
2 ,
505 -
512
-
27)
-
W. Ren
.
On consensus algorithms for double-integrator dynamics.
IEEE Trans. Autom. Control
,
6 ,
1503 -
1509
-
28)
-
Y. Cao ,
W. Ren
.
Sampled-data discrete-time coordination algorithms for double-integrator dynamics under dynamic directed interaction.
Int. J. Control
,
3 ,
506 -
515
-
29)
-
A. Jadbabaie ,
J. Lin ,
A.S. Morse
.
Coordination of groups of mobile autonomous agents using nearest neighbor rules.
IEEE Trans. Autom. Control
,
6 ,
988 -
1001
-
30)
-
L. Moreau
.
Stability of multi-agent systems with time-dependent communication links.
IEEE Trans. Autom. Control
,
2 ,
169 -
182
-
31)
-
Ren, W., Cao, Y.: `Convergence of sampled-data consensus algorithms for double-integrator dynamics', Proc. IEEE Conf. on Decision and Control, December 2008, Cancun, Mexico, p. 3965–3970.
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2010.0397
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