×
Lu, Xiaoqing; Austin, Francis; Chen, Shihua

Formation control for second-order multi-agent systems with time-varying delays under directed topology. (English) Zbl 1239.93005

Commun. Nonlinear Sci. Numer. Simul. 17, No. 3, 1382-1391 (2012).
Summary: In this paper, we investigate a formation control problem for second-order multi-agent systems with directed graph interconnection topologies that contain time-varying coupling delays. By using a special multiple leaders’ framework, sufficient conditions are obtained for both time-invariant and time-varying formations as well as for time-varying formations for trajectory tracking, which guarantees that the attainment of the formations is exponentially converging. Some numerical simulations are also conducted to validate the theoretical results.

Cited in 24 Documents

MSC:

93A14 Decentralized systems
93C15 Control/observation systems governed by ordinary differential equations
34H05 Control problems involving ordinary differential equations

Keywords:

multi-agent system; time-varying delay; second-order systems; formation control; directed topology
Cite Review PDF
Full Text: DOI

References:

[1] Liu, X. W.; Chen, T. P.; Lu, W. W., Consensus problem in directed networks of multi-agents via nonlinear protocols, Phys Lett A, 373, 3122-3127 (2009) · Zbl 1233.34012
[2] Yu, W. W.; Chen, G. R.; Lü, J. H., On pinning synchronization of complex dynamical networks, Automatica, 45, 429-435 (2009) · Zbl 1158.93308
[3] Lu, X. Q.; Austin, F.; Chen, S. H., Flocking in multi-agent systems with active virtual leader and time-varying delays coupling, Commun Nonlinear Sci Numer Simulat, 16, 1024-1026 (2011) · Zbl 1221.93193
[4] Hong, Y. G.; Hu, J. P.; Gao, L. X., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 1177-1182 (2006) · Zbl 1117.93300
[5] Saber, R. O.; Murray, R., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans Automat Control, 49, 1520-1533 (2004) · Zbl 1365.93301
[6] Su, H. S.; Wang, X. F., Flocking of multi-agents with a virtual leader, IEEE Trans Automat Control, 54, 293-307 (2009) · Zbl 1367.37059
[7] Moreau, L., Stability of multi-agent systems with time-dependent communication links, IEEE Trans Automat Control, 50, 169-182 (2005) · Zbl 1365.93268
[8] Hu, J. P.; Hong, Y. G., Leader-following coordination of multi-agent systems with coupling time delays, Physica A, 374, 853-863 (2007)
[9] Xiao, F.; Wang, L.; Chen, J.; Gao, Y. P., Finite-time formation control for multi-agent systems, Automatica, 45, 2606-2611 (2009) · Zbl 1180.93006
[10] Jiang, F.; Wang, L., Finite-time information consensus for multi-agent systems with fixed and switching topologies, Physica D, 238, 1550-1560 (2009) · Zbl 1170.93304
[11] Dimarogonasa, D.; Johansson, K., Stability analysis for multi-agent systems using the incidence matrix: quantized communication and formation control, Automatica, 46, 695-700 (2010) · Zbl 1193.93059
[12] Kristian, H.; Stjepan, B.; Ivica, D., Multi-agent formation control based on bell-shaped potential functions, J Intell Robot Syst, 58, 165-189 (2010) · Zbl 1203.68293
[13] Wu, C., Synchronization in complex networks of nonlinear dynamical systems (2007), World Scientific · Zbl 1135.34002
[14] Horn, R.; Jornson, C., Matrix analysis (1985), Cambridge University Press: Cambridge University Press New York · Zbl 0576.15001
[15] Lu, X. Q.; Austin, F.; Chen, S. H., Cluster consensus of second-order multi-agent systems via pinning control, Chin Phys B, 12, 120506 (2010)
[16] Hale, J.; Lunel, S., Introduction to the theory of functional differential equations, Applied Mathematical Sciences (1991), Springer: Springer New York
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.