×

zbMATH — the first resource for mathematics

Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays. (English) Zbl 1133.68412
Summary: We discuss average consensus problem in undirected networks of dynamic agents with fixed and switching topologies as well as multiple time-varying communication delays. By employing a linear matrix inequality method, we prove that all the nodes in the network achieve average consensus asymptotically for appropriate communication delays if the network topology is connected. Particularly, several feasible linear matrix inequalities are established to determine the maximal allowable upper bound of time-varying communication delays. Numerical examples are given to demonstrate the effectiveness and the sharpness of the theoretical results.

MSC:
68T05 Learning and adaptive systems in artificial intelligence
Software:
LMI toolbox
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] R. W. Beard, V. Stepanyan, Synchronization of information in distributed multiple vehicle coordination control, in: Proceedings of the IEEE Conference on Decision and Control, Maui, HI. December 2003, pp. 2029-2034.
[2] Boyd, B.; Ghaoui, L.E.; Feron, E.; Balakrishnan, V., Linear matrix inequalities in system and control theory, (1994), SIAM Philadelphia, PA · Zbl 0816.93004
[3] T. Chu, L. Wang, T. Chen, Self-organized motion in a class of anisotropic swarms, in: Proceedings of American Control Conference, Portland, OR, USA, June 2005, pp. 3474-3479.
[4] Fax, J.A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE trans. automat. control, 49, 1465-1476, (2004) · Zbl 1365.90056
[5] Gahinet, P.; Nemirovski, A.; Laub, A.; Chilali, M., LMI control toolbox User’s guide. the math works, (1995), Natick MA
[6] Hale, J.K.; Verduyn Lunel, S.M., Introduction to functional differential equations, (1993), Springer New York · Zbl 0787.34002
[7] Jadbabaie, A.; Lin, J.; Morse, A.S., Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE trans. automat. control, 48, 988-1001, (2003) · Zbl 1364.93514
[8] Lawton, J.R.; Beard, R.W., Synchronized multiple spacecraft rotations, Automatica, 38, 1359-1364, (2002) · Zbl 1032.93553
[9] Lin, Z.; Broucke, M.; Francis, B., Local control strategies for groups of mobile autonomous agents, IEEE trans. automat. control, 49, 622-629, (2004) · Zbl 1365.93208
[10] Liu, B.; Chu, T.; Wang, L.; Wang, Z., Swarm dynamics of a group of mobile autonomous agents, Chinese phys. lett., 22, 254-257, (2005)
[11] Lynch, N.A., Distributed algorithms, morgan kaufmann, (1997), San Mateo CA
[12] L. Moreau, Stability of continuous-time distributed consensus algorithms, in: Proceedings of the IEEE Conference Decision and Control, Atlantis, Paradise Island, Bahamas, 2004, pp. 3998-4003.
[13] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE trans. automat. control, 50, 169-182, (2005) · Zbl 1365.93268
[14] Mu, S.; Chu, T.; Wang, L., Coordinated collective motion in a motile particle group with a leader, Phys. A, 351, 211-226, (2005)
[15] Olfati-Saber, R.; Murray, R.M., Consensus problems in networks of agents with switching topology and time-delays, IEEE trans. automat. control, 49, 1520-1533, (2004) · Zbl 1365.93301
[16] Ren, W.; Beard, R.W., Consensus seeking in multiagent systems under dynamically changing interaction topologies, IEEE trans. automat. control, 50, 655-661, (2005) · Zbl 1365.93302
[17] W. Ren, R. W. Beard, and E. M. Atkins, A survey of consensus problems in multi-agent coordination, in: Proceedings of the American Control Conference, Portland, 2005, pp. 1859-1864.
[18] Shi, H.; Wang, L.; Chu, T., Swarming behavior of multi-agent systems, J. control theory appl., 2, 313-318, (2004)
[19] Toner, J.; Tu, Y., Flocks, herds, and schools: a quantitative theory of flocking, Phys. rev. E, 75, 1226-1229, (1995)
[20] L. Wang, H. Shi, T. Chu, W. Zhang, L. Zhang, Aggregation of foraging swarms, Lecture Notes in Computer Science vol. 3339, Springer, 2004, pp. 766-777.
[21] Xiao, L.; Boyd, S., Fast linear iterations for distributed averaging, Systems control lett., 53, 65-78, (2004) · Zbl 1157.90347
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.