## Abstract and Applied Analysis

### Adjacent-Compensation Consensus Algorithm in Asynchronously Coupled Form for Second-Order Multiagent Network under Communication Delay

#### Abstract

General asynchronously coupled consensus algorithm associated with adjacent compensations, is proposed to solve the dynamical consensus problem of second-order multiagent network with communication delay under leader-following coordination control framework. Based on frequency-domain analysis, firstly, delay-independent consensus convergence is proved for the second-order multiagent systems with a spanning tree topology that has the leader root and then delay-dependent consensus condition is obtained for the multiagent systems with communication delay under a general leader-following interconnection topology. Simulation illustrates the correctness of the results.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 974129, 7 pages.

Dates
First available in Project Euclid: 2 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412273180

Digital Object Identifier
doi:10.1155/2014/974129

Mathematical Reviews number (MathSciNet)
MR3173300

Zentralblatt MATH identifier
07023433

#### Citation

Liu, Cheng-Lin; Liu, Fei. Adjacent-Compensation Consensus Algorithm in Asynchronously Coupled Form for Second-Order Multiagent Network under Communication Delay. Abstr. Appl. Anal. 2014 (2014), Article ID 974129, 7 pages. doi:10.1155/2014/974129. https://projecteuclid.org/euclid.aaa/1412273180

#### References

• A. Jadbabaie, J. Lin, and A. S. Morse, “Coordination of groups of mobile autonomous agents using nearest neighbor rules,” IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988–1001, 2003.
• R. Olfati-Saber and R. M. Murray, “Consensus problems in networks of agents with switching topology and time-delays,” IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1520–1533, 2004.
• W. Ren and R. W. Beard, “Consensus seeking in multiagent systems under dynamically changing interaction topologies,” IEEE Transactions on Automatic Control, vol. 50, no. 5, pp. 655–661, 2005.
• W. Ren and E. Atkins, “Distributed multi-vehicle coordinated control via local information exchange,” International Journal of Robust and Nonlinear Control, vol. 17, no. 10-11, pp. 1002–1033, 2007.
• Y. G. Hong, L. X. Gao, D. Z. Cheng, and J. Hu, “Lyapunov-based approach to multiagent systems with switching jointly connected interconnection,” IEEE Transactions on Automatic Control, vol. 52, no. 5, pp. 943–948, 2007.
• L. Gao, J. Zhang, and W. Chen, “Second-order consensus for multiagent systems under directed and switching topologies,” Mathematical Problems in Engineering, vol. 2012, Article ID 273140, 21 pages, 2012.
• P. Lin, Y. Jia, J. Du, and S. Yuan, “Distributed consensus control for second-order agents with fixed topology and time-delay,” in Proceedings of the 26th Chinese Control Conference (CCC '07), pp. 577–581, July 2007.
• W. Yu, G. Chen, and M. Cao, “Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems,” Automatica, vol. 46, no. 6, pp. 1089–1095, 2010.
• J. Hu and Y. Hong, “Leader-following coordination of multi-agent systems with coupling time delays,” Physica A, vol. 374, no. 2, pp. 853–863, 2007.
• H. Su and X. Wang, “Second-order consensus of multiple agents with coupling delay,” in Proceedings of the 7th world Congress on Intelligent Control and Automation (WCICA '08), pp. 7177–7180, June 2008.
• P. Lin, Y. Jia, and L. Li, “Distributed robust ${H}_{\infty }$ consensus con-trol in directed networks of agents with time-delay,” Systems & Control Letters, vol. 57, no. 8, pp. 643–653, 2008.
• Y. G. Sun, L. Wang, and G. Xie, “Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays,” Systems & Control Letters, vol. 57, no. 2, pp. 175–183, 2008.
• J. Qin, H. Gao, and W. X. Zheng, “Second-order consensus for multi-agent systems with switching topology and communication delay,” Systems & Control Letters, vol. 60, no. 6, pp. 390–397, 2011.
• J. Yu and L. Wang, “Group consensus in multi-agent systems with switching topologies and communication delays,” Systems & Control Letters, vol. 59, no. 6, pp. 340–348, 2010.
• Z. Tang, T. Huang, J. Hu, and J.-L. Shao, “Leader-following con-sensus in networks of agents with nonuniform time-varying delays,” Mathematical Problems in Engineering, vol. 2012, Article ID 848942, 14 pages, 2012.
• J. Wang and N. Elia, “Consensus over networks with dynamic channels,” in Proceedings of the American Control Conference (ACC '08), pp. 2637–2642, June 2008.
• D. J. Lee and M. W. Spong, “Agreement with non-uniform infor-mation delays,” in Proceedings of the American Control Conference (ACC '06), pp. 756–761, June 2006.
• L. Moreau, “Stability of continuous-time distributed consensus algorithms,” in Proceedings of the 43rd IEEE Conference on Decision and Control (CDC), pp. 3998–4003, December 2004.
• W. Wang and J.-J. E. Slotine, “Contraction analysis of time-delayed communications and group cooperation,” IEEE Transactions on Automatic Control, vol. 51, no. 4, pp. 712–717, 2006.
• N. Chopra and M. K. Spong, “Passivity-based control of multi-agent systems,” in Advances in Robot Control: From Everyday Physics to Human-Like Movements, pp. 107–134, Springer, New York, NY, USA, 2006.
• M. Cao, A. S. Morse, and B. D. O. Anderson, “Reaching an agreement using delayed information,” in Proceedings of the 45th IEEE Conference on Decision and Control (CDC '06), pp. 3375–3380, December 2006.
• L. Wang and F. Xiao, “A new approach to consensus problems for discrete-time multiagent systems with time-delays,” in Pro-ceedings of the American Control Conference (ACC '06), pp. 2118–2123, June 2006.
• P. Lin and Y. Jia, “Consensus of second-order discrete-time multi-agent systems with nonuniform time-delays and dynamically changing topologies,” Automatica, vol. 45, no. 9, pp. 2154–2158, 2009.
• C.-L. Liu and F. Liu, “Stationary consensus of heterogeneous multi-agent systems with bounded communication delays,” Automatica, vol. 47, no. 9, pp. 2130–2133, 2011.
• W. Yang, A. L. Bertozzi, and X. Wang, “Stability of a second order consensus algorithm with time delay,” in Proceedings of the 47th IEEE Conference on Decision and Control (CDC '08), pp. 2926–2931, December 2008.
• C.-L. Liu and F. Liu, “Asynchronously-coupled consensus of sec-ond-order dynamic agents with communication delay,” International Journal of Innovative Computing, Information and Con-trol, vol. 6, no. 11, pp. 5035–5046, 2010.
• U. Münz, A. Papachristodoulou, and F. Allgöwer, “Delay robustness in consensus problems,” Automatica, vol. 46, no. 8, pp. 1252–1265, 2010.
• C.-L. Liu and F. Liu, “Dynamical consensus seeking of second-order multi-agent systems based on delayed state compensation,” Systems & Control Letters, vol. 61, no. 12, pp. 1235–1241, 2012. \endinput