© The Institution of Engineering and Technology
In this study, the consensus problem for a class of second-order multi-agent systems (MASs) with Markovian characterisations is investigated. The stochastic switching topology and the random communication delay are dominated by two mutually independent Markov chains. The communication delay exists in the switching signal as well as the position information exchanges in the authors’ work. A novel consensus protocol is presented without using the neighbours’ velocity information. By performing three steps of model transformation and introducing a mapping for the two independent Markov chains, the original system is converted into an expanded analogous error system with two Markovian jumping parameters. A necessary and sufficient criterion for the mean square consensus of the Markovian jump second-order MASs with random communication delay is derived. Finally, a numerical example is given to illustrate the feasibility and effectiveness of the theoretical result.
References
-
-
1)
-
6. Ren, W., Beard, R., McLain, T.: ‘Coordination variables and consensus building in multiple vehicle systems’, in Kumar, V., Leonard, N., Morse, A. (Eds): ‘Cooperative control: lecture notes in control and information science’ (Springer, Berlin Heidelberg, 2005), Vol. 309, pp. 171–188.
-
2)
-
23. Zhang, Q., Chen, S., Yu, C.: ‘Impulsive consensus problem of second-order multi-agent systems with switching topologies’, Commun. Nonlinear Sci. Numer. Simul., 2012, 17, (1), pp. 9–16 (doi: 10.1016/j.cnsns.2011.04.007).
-
3)
-
R. Olfati-Saber
.
Flocking for multi-agent dynamic systems: algorithms and theory.
IEEE Trans. Autom. Control
,
3 ,
401 -
420
-
4)
-
19. Su, Y., Huang, J.: ‘Two consensus problems for discrete-time multi-agent systems with switching network topology’, Automatica, 2012, 48, (9), pp. 1988–1997 (doi: 10.1016/j.automatica.2012.03.029).
-
5)
-
26. You, K., Li, Z., Xie, L.: ‘Consensus for general multi-agent systems over random graphs’. 2011 9th IEEE Int. Conf. on Control and Automation (ICCA), 2011, pp. 830–835.
-
6)
-
18. You, K.Y., Li, Z.K., Xie, L.H.: ‘Consensus condition for linear multi-agent systems over randomly switching topologies’, Automatica, 2013, 49, (10), pp. 3125–3132 (doi: 10.1016/j.automatica.2013.07.024).
-
7)
-
P. Lin ,
Y. Jia
.
Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies.
Automatica
,
2154 -
2158
-
8)
-
31. Qin, J., Gao, H., Zheng, W.X.: ‘Second-order consensus for multi-agent systems with switching topology and communication delay’, Systems Control Lett., 2011, 60, (6), pp. 390–397 (doi: 10.1016/j.sysconle.2011.03.004).
-
9)
-
G. Wen ,
Z. Duan ,
W. Yu ,
G. Chen
.
Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: a delayed-input approach.
Int. J. Robust Nonlinear Control
-
10)
-
Z.K. Li ,
Z.S. Duan ,
G.R. Chen ,
L. Huang
.
Consensus of multi-agent systems and synchronization of complex networks: a unified viewpoint.
IEEE Trans. Cir. Syst. I, Reg. Papers
,
1 ,
213 -
224
-
11)
-
9. Bauso, D., Giarre, L., Pesenti, R.: ‘Distributed consensus protocols for coordinating buyers’. Decision and Control, 2003. Proc. 42nd IEEE Conf., December 2003, 1, pp. 588–592.
-
12)
-
24. Ya, Z.: ‘Consensus of multi-agent systems with stochastic switching topology’, Twenty-seventh Chinese Control Conf 2008. CCC 2008., 2008, pp. 545–549.
-
13)
-
J.A. Fax ,
R.M. Murray
.
Information flow and cooperative control of vehicle formations.
IEEE Trans. Autom. Control
,
9 ,
1465 -
1476
-
14)
-
4. Ren, W.: ‘Distributed attitude alignment in spacecraft formation flying’, Int. J. Adapt. Control Signal Process., 2007, 21, (2-3), pp. 95–113.
-
15)
-
17. Sun, F., Guan, Z.-H., Zhan, X.-S., Yuan, F.-S.: ‘Consensus of second-order and high-order discrete-time multi-agent systems with random networks’, Nonlinear Anal., Real World Appl., 2012, 13, (5), pp. 1979–1990 (doi: 10.1016/j.nonrwa.2011.12.009).
-
16)
-
33. Wang, Y.-W., Bian, T., Xiao, J.-W., Huang, Y.: ‘Robust synchronization of complex switched networks with parametric uncertainties and two types of delays’, Int. J. Robust Nonlinear Control, 2013, 23, (2), pp. 190–207 (doi: 10.1002/rnc.1824).
-
17)
-
15. Liu, Z.-W., Guan, Z.-H., Li, T., Zhang, X.-H., Xiao, J.-W.: ‘Quantized consensus of multi-agent systems via broadcast gossip algorithms’, Asian J. Control, 2012, 14, (6), pp. 1634–1642 (doi: 10.1002/asjc.525).
-
18)
-
12. Cao, Y., Ren, W.: ‘Distributed coordinated tracking with reduced interaction via a variable structure approach’, IEEE Trans. Autom. Control, 2012, 57, (1), pp. 33–48 (doi: 10.1109/TAC.2011.2146830).
-
19)
-
5. Lin, J., Morse, A., Anderson, B.: ‘The multi-agent rendezvous problem’. Proc. of 42nd IEEE Conf. on Decision and Control, 2003, 2, pp. 1508–1513 (doi: 10.1109/CDC.2003.1272825).
-
20)
-
W. Yu ,
G. Chen ,
M. Cao
.
Distributed leader-follower flocking control for multi-agent dynamical systems with time-varying velocities.
Syst. Control Lett.
,
9 ,
543 -
552
-
21)
-
Y. Zhang ,
Y. Tian
.
Consentability and protocol design of multi-agent systems with stochastic switching topology.
Automatica
,
5 ,
1195 -
1201
-
22)
-
29. Miao, G., Xu, S., Zou, Y.: ‘Necessary and sufficient conditions for mean square consensus under Markov switching topologies’, Int. J. Syst. Sci., 2013, 44, (1), pp. 178–186 (doi: 10.1080/00207721.2011.598961).
-
23)
-
J.H. Seo ,
J. Back ,
H. Kim ,
H. Shim
.
Output feedback consensus for high-order linear systems having uniform ranks under switching topology.
IET Control Theory Appl.
,
8 ,
1118 -
1124
-
24)
-
T. Li ,
J.F. Zhang
.
Consensus conditions of multi-agent systems with time-varying topologies and stochastic communication noises.
IEEE Trans. Autom. Control
,
9 ,
2043 -
2057
-
25)
-
32. Tang, Z.-J., Huang, T.-Z., Shao, J.-L., Hu, J.-P.: ‘Consensus of second-order multi-agent systems with nonuniform time-varying delays’, Neurocomputing, 2012, 97, pp. 410–414 (doi: 10.1016/j.neucom.2012.05.025).
-
26)
-
19. Xie, G., Wang, L.: ‘Consensus control for a class of networks of dynamic agents: switching topology’. American Control Conf., 2006, p. 6.
-
27)
-
10. Alanyali, M., Venkatesh, S., Savas, O., Aeron, S.: ‘Distributed Bayesian hypothesis testing in sensor networks’. Proc. of the American Control Conf., 2004, Vol. 6, pp. 5369–5374.
-
28)
-
M. Liu ,
D.W.C. Ho ,
Y. Niu
.
Stabilization of Markovian jump linear system over networks with random communication delay.
Automatica
,
2 ,
416 -
421
-
29)
-
T. Li ,
J. Zhang
.
Mean square average-consensus under measurement noises and fixed topologies: necessary and sufficient conditions.
Automatica
,
1929 -
1936
-
30)
-
8. Lawton, J.R., Beard, R.W.: ‘Synchronization multiple spacecraft rotations’, Automatica, 2002, 38, (8), pp. 1359–1364 (doi: 10.1016/S0005-1098(02)00025-0).
-
31)
-
Z. Lin ,
B.A. Francis ,
M. Maggiore
.
Necessary and sufficient graphical conditions for formation control of unicycles.
IEEE Trans. Autom. Control
,
121 -
127
-
32)
-
J.H. Seo ,
H. Shim ,
J. Back
.
Consensus of high-order linear systems using dynamic output feedback compensator: low gain approach.
Automatica
,
2659 -
2664
-
33)
-
27. Zhao, H., Xu, S., Yuan, D.: ‘Consensus of data-sampled multi-agent systems with Markovian switching topologies’, Asian J. Control, 2012, 14, (5), pp. 1366–1373 (doi: 10.1002/asjc.444).
-
34)
-
18. Matei, I., Baras, J.S., Somarakis, C.: ‘Convergence results for the linear consensus problem under Markovian random graphs’, SIAM J. Control Opt., 2013, 51, (2), pp. 1574–1591 (doi: 10.1137/100816870).
-
35)
-
29. Lin, P., Jia, Y.: ‘Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies’, IEEE Trans. Autom. Control, 2010, 55, (3), pp. 778–784 (doi: 10.1109/TAC.2010.2040500).
-
36)
-
J. Xiong ,
J. Lam
.
Stabilization of discrete-time Markovian jump linear systems via time-delayed controllers.
Automatica
,
747 -
753
http://iet.metastore.ingenta.com/content/journals/10.1049/iet-cta.2014.0057
Related content
content/journals/10.1049/iet-cta.2014.0057
pub_keyword,iet_inspecKeyword,pub_concept
6
6