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Second-order consensus in multi-agent dynamical systems with sampled position data. (English) Zbl 1220.93005
Summary: This paper studies second-order consensus in multi-agent dynamical systems with sampled position data. A distributed linear consensus protocol with second-order dynamics is designed, where both the current and some sampled past position data are utilized. It is found that second-order consensus in such a multi-agent system cannot be reached without any sampled position data under the given protocol while it can be achieved by appropriately choosing the sampling period. A necessary and sufficient condition for reaching consensus of the system in this setting is established, based on which consensus regions are then characterized. It is shown that if all the eigenvalues of the Laplacian matrix are real, then second-order consensus in the multi-agent system can be reached for any sampling period except at some critical points depending on the spectrum of the Laplacian matrix. However, if there exists at least one eigenvalue of the Laplacian matrix with a nonzero imaginary part, second-order consensus cannot be reached for sufficiently small or sufficiently large sampling periods. In such cases, one nevertheless may be able to find some disconnected stable consensus regions determined by choosing appropriate sampling periods. Finally, simulation examples are given to verify and illustrate the theoretical analysis.

93A14 Decentralized systems
93B60 Eigenvalue problems
Full Text: DOI
[1] Arenas, A.; Diaz-Guilera, A.; Kurths, J.; Moreno, Y.; Zhou, C., Synchronization in complex networks, Physics reports, 468, 3, 93-153, (2008)
[2] Bertsekas, D.P.; Tsitsiklis, J.N., Parallel and distributed computation: numerical methods, (1989), Prentice-Hall Englewood Cliffs, NJ · Zbl 0743.65107
[3] Cao, M.; Morse, A.S.; Anderson, B.D.O., Reaching a consensus in a dynamically changing environment: a graphical approach, SIAM journal on control and optimization, 47, 2, 575-600, (2008) · Zbl 1157.93514
[4] Cao, Y., Ren, W., & Chen, Y. (2008). Multi-agent consensus using both current and outdated states. In Proceedings of the 17th world congress IFAC (pp. 2874-2879).
[5] DeGroot, M.H., Reaching a consensus, Journal of the American statistical association, 69, 345, 118-121, (1974) · Zbl 0282.92011
[6] Duan, Z.; Chen, G.; Huang, L., Disconnected synchronized regions of complex dynamical networks, IEEE transactions on automatic control, 54, 4, 845-849, (2009) · Zbl 1367.93461
[7] Fiedler, M., Algebraic connectivity of graphs, Czechoslovak mathematical journal, 23, 2, 298-305, (1973) · Zbl 0265.05119
[8] Godsil, C.; Royle, G., Algebraic graph theory, (2001), Springer-Verlag New York · Zbl 0968.05002
[9] Hong, Y.; Chen, G.; Bushnell, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850, (2008) · Zbl 1283.93019
[10] Hong, Y.; Hu, J.; Gao, L., Tracking control for multi-agent consensus with an active leader and variable topology, Automatica, 42, 7, 1177-1182, (2006) · Zbl 1117.93300
[11] Horn, R.A.; Johnson, C.R., Matrix analysis, (1985), Cambridge University Press Cambridge, UK · Zbl 0576.15001
[12] Horn, R.A.; Johnson, C.R., Topics in matrix analysis, (1991), Cambridge University Press Cambridge, UK · Zbl 0729.15001
[13] Gazi, V.; Passino, K.M., Stability analysis of swarms, IEEE transactions on automatic control, 48, 4, 692-697, (2003) · Zbl 1365.92143
[14] 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, 985-1001, (2003) · Zbl 1364.93514
[15] Liu, C.; Duan, Z.; Chen, G.; Huang, L., Analyzing and controlling the network synchronization regions, Physica A, 386, 1, 531-542, (2007)
[16] Lü, J.; Chen, G., A time-varying complex dynamical network models and its controlled synchronization criteria, IEEE transactions on automatic control, 50, 6, 841-846, (2005) · Zbl 1365.93406
[17] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE transactions on automatic control, 50, 2, 169-182, (2005) · Zbl 1365.93268
[18] Olfati-Saber, R., 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
[19] Olfati-Saber, R., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE transactions on automatic control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[20] Parks, P.C.; Hahn, V., Stability theory, (1993), Prentice Hall · Zbl 0757.34041
[21] Pecora, L.M.; Carroll, T.L., Synchronization in chaotic systems, Physical review letters, 64, 8, 821-824, (1990) · Zbl 0938.37019
[22] Ren, W., On consensus algorithms for double-integrator dynamics, IEEE transactions on automatic control, 58, 6, 1503-1509, (2008) · Zbl 1367.93567
[23] Ren, W.; Atkins, E., Distributed multi-vehicle coordinated control via local information exchange, International journal of robust and nonlinear control, 17, 10-11, 1002-1033, (2007) · Zbl 1266.93010
[24] Ren, W.; Beard, R.W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE transactions on automatic control, 50, 5, 655-661, (2005) · Zbl 1365.93302
[25] Reynolds, C.W., Flocks, herds, and schools: a distributed behavior model, Computer graphics, 21, 4, 25-34, (1987)
[26] Vicsek, T.; Cziok, A.; Jacob, E.B.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Physical review letters, 75, 6, 1226-1229, (1995)
[27] Wang, X.; Chen, G., Synchronization in scale-free dynamical networks: robustness and fragility, IEEE transactions on circuits and systems I, 49, 1, 54-62, (2002) · Zbl 1368.93576
[28] Yu, W.; Cao, J.; Lü, J., Global synchronization of linearly hybrid coupled networks with time-varying delay, SIAM journal on applied dynamical systems, 7, 1, 108-133, (2008) · Zbl 1161.94011
[29] 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
[30] Yu, W.; Chen, G.; Cao, M.; Kurths, J., Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE transactions on systems, man, and cybernetics, part B, 40, 3, 881-891, (2010)
[31] Yu, W.; Chen, G.; Lü, J., On pinning synchronization of complex dynamical networks, Automatica, 45, 2, 429-435, (2009) · Zbl 1158.93308
[32] Yu, W., Chen, G., & Ren, W. (2010). Delay-induced quasi-consensus in multi-agent dynamical systems. In 29th Chinese control conference, Beijing, China (pp. 4566-4571).
[33] Yu, W., Chen, G., Ren, W., Kurths, J., & Zheng, W. X. (2011). Distributed higher-order consensus protocols in multi-agent dynamical systems. IEEE Transactions on Circuits and Systems I (in press) doi:10.1109/TCSI.2011.2106032.
[34] Yu, W.; Chen, G.; Wang, Z.; Yang, W., Distributed consensus filtering in sensor networks, IEEE transactions on systems, man, and cybernetics, part B, 39, 6, 1568-1577, (2009)
[35] Zhou, J.; Lu, J.; Lü, J., Adaptive synchronization of an uncertain complex dynamical network, IEEE transactions on automatic control, 51, 4, 652-656, (2006) · Zbl 1366.93544
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