×

Consensus of second-order discrete-time multi-agent systems with fixed topology. (English) Zbl 1231.93007

Summary: This paper studies the consensus of second-order discrete-time multi-agent systems with fixed topology. First, we formulate the problem and give some preliminaries. Then, by algebraic graph theory and matrix theory, the convergence of system matrix is analyzed. Our main results indicate that the consensus of second-order system can be achieved if and only if the topology graph has a directed spanning tree and the values of the scaling parameters are in a fixed range. The eigenvalues of the corresponding Laplacian matrix play a key role to reach consensus. Finally, numerical simulations are given to illustrate the results.

MSC:

93A14 Decentralized systems
93C55 Discrete-time control/observation systems
94C15 Applications of graph theory to circuits and networks
93B60 Eigenvalue problems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lynch, N. A., Distributed Algorithms (1996), Morgan Kaufmann Publishers · Zbl 0877.68061
[2] DeGroot, M. H., Reaching a consensus, J. Amer. Statist. Assoc., 69, 345, 118-121 (1974) · Zbl 0282.92011
[3] Borkar, V.; Varaiya, P. P., Asymptotic agreement in distributed estimation, IEEE Trans. Automat. Control, 27, 3, 650-655 (1982) · Zbl 0497.93037
[4] Tsitsiklis, J. N.; Athans, M., Convergence and asymptotic agreement in distributed decision problems, IEEE Trans. Automat. Control, 29, 1, 42-50 (1984) · Zbl 0535.90006
[5] Tsitsiklis, J. N.; Bertsekas, D. P.; Athans, M., Distributed asynchronous deterministic and stochastic gradient optimization algorithms, IEEE Trans. Automat. Control, 31, 9, 803-812 (1986) · Zbl 0602.90120
[6] Vicsek, T.; Czirok, A.; Jacob, E. B.; Cohen, I.; Shochet, O., Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75, 6, 1226-1229 (1995)
[7] Fax, J. A.; Murray, R. M., Information flow and cooperative control of vehicle formations, IEEE Trans. Automat. Control, 49, 9, 1465-1476 (2004) · Zbl 1365.90056
[8] Jadbabaie, A.; Lin, J.; Morse, A. S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. Automat. Control, 48, 6, 988-1001 (2003) · Zbl 1364.93514
[9] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE Trans. Automat. Control, 50, 2, 169-182 (2005) · Zbl 1365.93268
[10] Olfati-Saber, R.; Murray, R. M., Consensus problems in networks of agents with switching topology and time-delays, IEEE Trans. Automat. Control, 49, 9, 1520-1533 (2004) · Zbl 1365.93301
[11] Fang, L.; Antsaklis, P. J., Information consensus of asynchronous discrete-time multi-agent systems, (Proc. American Control Conference (2005), Institune of Electrical and Electronics Engineering), 1883-1888
[12] Xiao, F.; Wang, L., State consensus for multi-agent systems with switching topologies and time-varying delays, Internat. J. Control, 79, 10, 1277-1284 (2006) · Zbl 1330.94022
[13] Ren, W.; Beard, R. W.; Atkins, E. M., Information consensus in multivehicle cooperative control, IEEE Control Syst. Mag., 27, 2, 71-82 (2007)
[14] Ren, W.; Beard, R. W.; McLain, T. W., Coordination variables and consensus building in multiple vehicle systems, (Kumar, V.; Leonard, N. E.; Morse, A. S., Cooperative Control: A Post-Workshop Volume 2003 Block Island Workshop on Cooperative Control. Cooperative Control: A Post-Workshop Volume 2003 Block Island Workshop on Cooperative Control, Lecture Notes in Control and Inform. Sci., vol. 309 (2005), Springer-Verlag Series), 171-188
[15] Ren, W.; Beard, R. W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE Trans. Automat. Control, 50, 5, 655-661 (2005) · Zbl 1365.93302
[16] Li, T.; Zhang, J. F., Mean square average-consensus under measurement noises and fixed topologies: Necessary and sufficient conditions, Automatica, 45, 1929-1936 (2009) · Zbl 1185.93006
[17] Chopra, N.; Spong, M. W., Passivity-based control of multi-agent systems, (Advances in Robot Control: From Everyday Physics to Human-Like Movements (2006), Springer-Verlag: Springer-Verlag Berlin), 107-134 · Zbl 1134.93308
[18] Hong, Y. G.; Chen, G. R.; Bushnell, L., Distributed observers design for leader-following control of multi-agent networks, Automatica, 44, 3, 846-850 (2008) · Zbl 1283.93019
[19] Shi, H.; Wang, L.; Chu, T. G., Virtual leader approach to coordinated control of multiple mobile agents with asymmetric interactions, Phys. D, 213, 1, 51-65 (2006) · Zbl 1131.93354
[20] Ren, W., Second-order consensus algorithm with extensions to switching topologies and reference models, (Proc. American Control Conference (2007), Institune of Electrical and Electronics Engineering), 1431-1436
[21] Ren, W.; Atkins, E., Distributed multi-vehicle coordinated control via local information exchange, Internat. J. Robust Nonlinear Control, 17, 10-11, 1002-1033 (2007) · Zbl 1266.93010
[22] Ren, W.; Beard, R. W., Distribute Consensus in Multi-Vehicle Cooperative Control (2008), Springer-Verlag: Springer-Verlag London · Zbl 1144.93002
[23] Zhu, J. D.; Tian, Y. P.; Kuang, J., On the general consensus protocol of multi-agent systems with double-integrator dynamics, Linear Algebra Appl., 431, 701-715 (2009) · Zbl 1165.93022
[24] W. Ren, E. Atkins, Second-order consensus protocols in multiple vehicle systems with local interactions, in: AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California, 2005.; W. Ren, E. Atkins, Second-order consensus protocols in multiple vehicle systems with local interactions, in: AIAA Guidance, Navigation, and Control Conference and Exhibit, San Francisco, California, 2005.
[25] Yu, W. W.; Chen, G. R.; Cao, M., Some necessary and sufficient conditions for second-order consensus in multi-agent dynamical systems, Automatica, 46, 1089-1095 (2010) · Zbl 1192.93019
[26] Yu, W. W.; Chen, G. R.; Cao, M.; Kurths, J., Second-order consensus for multiagent systems with directed topologies and nonlinear dynamics, IEEE Trans. Syst. Man Cybernetics, 40, 3, 881-891 (2010)
[27] Zhang, Y.; Tian, Y. P., Consentability and protocol design of multi-agent systems with stochastic switching topology, Automatica, 45, 1195-1201 (2009) · Zbl 1162.94431
[28] Ogata, K., Discrete-Time Control Systems (1995), Prentice-Hall: Prentice-Hall Englewood Cliffs, NJ
[29] G.M. Xie, H.Y. Liu, L. Wang, Y.M. Jia, Consensus in networked multi-agent systems via sampled control: Fixed topology case, in: 2009 American Control Conference, 2009, pp. 3902-3907.; G.M. Xie, H.Y. Liu, L. Wang, Y.M. Jia, Consensus in networked multi-agent systems via sampled control: Fixed topology case, in: 2009 American Control Conference, 2009, pp. 3902-3907.
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.