Consensus analysis for high-order multi-agent systems without or with delays. (English) Zbl 1417.93051
Summary: This paper studies the consensus problem for a high-order multi-agent systems without or with delays. Consensus protocols, which only depend on the own partial information of agents and partial relative information with its neighbors, are proposed for consensus and quasi-consensus, respectively. Firstly, some lemmas are presented, and then a necessary and sufficient condition for guaranteeing the consensus is established under the consensus protocol without delays. Furthermore, communication delays are considered. Some necessary and sufficient conditions for solving quasi-consensus problem with delays are obtained. Finally, some simulations are given to verify the theoretical results.
MSC:
| 93A14 | Decentralized systems |
| 94C15 | Applications of graph theory to circuits and networks |
| 68T42 | Agent technology and artificial intelligence |
| 93C65 | Discrete event control/observation systems |
References:
| [1] | Vicsek, T.; Czirk, A.; Ben-Jacob, E.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Physical Review Letters, 75, 6, 1226-1229 (1995) · doi:10.1103/PhysRevLett.75.1226 |
| [2] | Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Transactions on Automatic Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514 · doi:10.1109/TAC.2003.812781 |
| [3] | Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Transactions on Automatic Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301 · doi:10.1109/TAC.2004.834113 |
| [4] | Ren, W.; Beard, R. W., Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE Transactions on Automatic Control, 50, 5, 655-661 (2005) · Zbl 1365.93302 · doi:10.1109/TAC.2005.846556 |
| [5] | Meng, Z.; Ren, W.; Cao, Y.; You, Z., Leaderless and leader-following consensus with communication and input delays under a directed network topology, IEEE Transactions on Systems, Man, and Cybernetics B, 41, 1, 75-88 (2011) · doi:10.1109/TSMCB.2010.2045891 |
| [6] | Xie, G.; Wang, L., Consensus control for a class of networks of dynamic agents, International Journal of Robust and Nonlinear Control, 17, 10-11, 941-959 (2007) · Zbl 1266.93013 · doi:10.1002/rnc.1144 |
| [7] | Ren, W., On consensus algorithms for double-integrator dynamics, IEEE Transactions on Automatic Control, 58, 6, 1503-1509 (2008) · Zbl 1367.93567 · doi:10.1109/TAC.2008.924961 |
| [8] | Wen, G.; Duan, Z.; Yu, W.; Chen, G., Consensus of second-order multi-agent systems with delayed nonlinear dynamics and intermittent communications, International Journal of Control, 86, 2, 322-331 (2013) · Zbl 1278.93016 · doi:10.1080/00207179.2012.727473 |
| [9] | Yu, W.; Chen, G.; Cao, M.; Kurths, J., Second-order consensus for multi-agent systems with directed topologies and nonlinear dynamics, IEEE Transactions on Systems, Man, and Cybernetics B, 40, 3, 881-891 (2010) · doi:10.1109/TSMCB.2009.2031624 |
| [10] | Yu, W.; Chen, G.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 6, 1089-1095 (2010) · Zbl 1192.93019 · doi:10.1016/j.automatica.2010.03.006 |
| [11] | Song, Q.; Cao, J.; Yu, W., Second-order leader-following consensus of nonlinear multi-agent systems via pinning control, Systems & Control Letters, 59, 9, 553-562 (2010) · Zbl 1213.37131 · doi:10.1016/j.sysconle.2010.06.016 |
| [12] | Zhu, W.; Cheng, D., Leader-following consensus of second-order agents with multiple time-varying delays, Automatica, 46, 12, 1994-1999 (2010) · Zbl 1205.93056 · doi:10.1016/j.automatica.2010.08.003 |
| [13] | Wen, G.; Duan, Z.; Yu, W.; Chen, G., Consensus in multi-agent systems with communication constraints, International Journal of Robust and Nonlinear Control, 22, 2, 170-182 (2012) · Zbl 1244.93018 · doi:10.1002/rnc.1687 |
| [14] | Wen, G.; Duan, Z.; Yu, W.; Chen, G., Consensus of multi-agent systems with nonlinear dynamics and sampled-data information: a delayed-input approach, International Journal of Robust and Nonlinear Control, 23, 6, 602-619 (2013) · Zbl 1273.93012 · doi:10.1002/rnc.2779 |
| [15] | Li, Z.; Duan, Z.; Chen, G.; Huang, L., Consensus of multiagent systems and synchronization of complex networks: a unified viewpoint, IEEE Transactions on Circuits and Systems I, 57, 1, 213-224 (2010) · Zbl 1468.93137 · doi:10.1109/TCSI.2009.2023937 |
| [16] | Ren, W.; Moore, K. L.; Chen, Y., High-order and model reference consensus algorithms in cooperative control of multivehicle systems, Journal of Dynamic Systems, Measurement and Control, 129, 5, 678-688 (2007) · doi:10.1115/1.2764508 |
| [17] | Jiang, F.; Wang, L.; Jia, Y., Consensus in leaderless networks of high-order-integrator agents, Proceedings of the American Control Conference (ACC ’09) |
| [18] | He, W.; Cao, J., Consensus control for high-order multi-agent systems, IET Control Theory & Applications, 5, 1, 231-238 (2011) · doi:10.1049/iet-cta.2009.0191 |
| [19] | Xiao, F.; Wang, L., Consensus problems for high-dimensional multi-agent systems, IET Control Theory & Applications, 1, 3, 830-837 (2007) · doi:10.1049/iet-cta:20060014 |
| [20] | Cai, N.; Xi, J.-X.; Zhong, Y.-S., Swarm stability of high-order linear time-invariant swarm systems, IET Control Theory & Applications, 5, 2, 402-408 (2011) · doi:10.1049/iet-cta.2009.0589 |
| [21] | Lin, P.; Jia, Y., Consensus of a class of second-order multi-agent systems with time-delay and jointly-connected topologies, IEEE Transactions on Automatic Control, 55, 3, 778-784 (2010) · Zbl 1368.93275 · doi:10.1109/TAC.2010.2040500 |
| [22] | Liu, C.; Liu, F., Consensus problem of coupled dynamic agents with communication delay, Proceedings of the 29th Chinese Control Conference (CCC ’10) |
| [23] | Liu, X.; Lu, W.; Chen, T., Consensus of multi-agent systems with unbounded time-varying delays, IEEE Transactions on Automatic Control, 55, 10, 2396-2401 (2010) · Zbl 1368.93470 · doi:10.1109/TAC.2010.2054770 |
| [24] | Sun, Y. G.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems & Control Letters, 57, 2, 175-183 (2008) · Zbl 1133.68412 · doi:10.1016/j.sysconle.2007.08.009 |
| [25] | Yu, W.; Chen, G.; Ren, W., Delay-induced quasi-consensus in multi-agent dynamical systems, Proceedings of the 29th Chinese Control Conference (CCC ’10) |
| [26] | Godsil, C.; Royle, G., Algebraic Graph Theory (2001), New York, NY, USA: Springer, New York, NY, USA · Zbl 0968.05002 · doi:10.1007/978-1-4613-0163-9 |
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.
