zbMATH — the first resource for mathematics

Group consensus in multi-agent systems with switching topologies and communication delays. (English) Zbl 1197.93096
Summary: Group consensus problems in networks of dynamic agents are addressed for two cases: (i) communication topologies are switching and the switching occurs among finite topologies arbitrarily; (ii) communication topologies are switching and the switching occurs among finite topologies arbitrarily, and there exist communication delays. We introduce double-tree-form transformations under which dynamic equations of agents are transformed into reduced-order systems. Based on the reduced-order systems, we obtain some analysis results for the two cases. In addition, we further investigate multi-group consensus as an extension of the group consensus, and present some analysis results by similar techniques. Simulation results are presented to demonstrate the effectiveness of the theoretical results.

93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93A14 Decentralized systems
Full Text: DOI
[1] R.W. Beard, V. Stepanyan, Synchronization of information in distributed multiple vehicle coordination control, in: Proc. IEEE Conf. Decision and Control, Maui, HI, Dec. 2003, pp. 2029-2034.
[2] Xiao, L.; Boyd, S., Fast linear iterations for distributed averaging, Systems control lett., 53, 65-78, (2004) · Zbl 1157.90347
[3] T. Chu, L. Wang, T. Chen, Self-organized motion in a class of anisotropic swarms, in: Proc. Amer. Control Conf., Portland, OR, USA, June 2005, pp. 3474-3479.
[4] Vicsek, T.; Czirok, A.; Jacob, E.B.; Cohen, I.; Schochet, O., Novel type of phase transitions in a system of self-driven particles, Phys. rev. lett., 75, 1226-1229, (1995)
[5] F. Xiao, L. Wang, Reaching agreement in finite time via continuous local state feedback, in: Proc. 26th Chinese Control Conf., 2007, pp. 711-715.
[6] Cao, M.; Morse, A.S.; Anderson, B.D.O., Agreeing asynchronously, IEEE trans. automat. control, 53, 8, 1826-1838, (2008) · Zbl 1367.93359
[7] 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
[8] 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
[9] 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
[10] Xiao, F.; Wang, L., Consensus protocols for discrete-time multi-agent systems with time-varying delays, Automatica, 44, 10, 2577-2582, (2008) · Zbl 1155.93312
[11] Xie, G.; Wang, L., Consensus control for a class of networks of dynamic agents, Internat. J. robust nonlinear control, 17, 10-11, 941-959, (2007) · Zbl 1266.93013
[12] Ren, W.; Atkins, E., Distributed multi-vehicle coordinated control via local information exchange, Int. J. robust & nonlin. control, 17, 10-11, 1002-1033, (2007) · Zbl 1266.93010
[13] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE trans. automat. control, 50, 169-182, (2005) · Zbl 1365.93268
[14] Sun, Y.; Wang, L.; Xie, G., Average consensus in networks of dynamic agents with switching topologies and multiple time-varying delays, Systems control lett., 57, 2, 175-183, (2008) · Zbl 1133.68412
[15] Xiao, F.; Wang, L., Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE trans. automat. control, 53, 8, 1804-1816, (2008) · Zbl 1367.93255
[16] Porfiri, M.; Stilwell, D.J., Consensus seeking over random weighted directed graphs, IEEE trans. automat. control, 52, 9, 1767-1773, (2007) · Zbl 1366.93330
[17] Tahbaz-Salehi, A.; Jadbabaie, A., A necessary and sufficient condition for consensus over random networks, IEEE trans. automat. control, 53, 3, 791-795, (2008) · Zbl 1367.90015
[18] Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proc. IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138
[19] W. Ren, R.W. Beard, E.M. Atkins, A survey of consensus problems in multi-agent coordination, in: Proc. Amer. Control Conf., Portland, 2005, pp. 1859-1864.
[20] Sun, Y.; Wang, L., Consensus of multi-agent systems in directed networks with nonuniform time-varying delays, IEEE trans. automat. control, 54, 7, 1607-1613, (2009) · Zbl 1367.93574
[21] J. Yu, L. Wang, Group consensus in multi-agent systems with undirected communication graphs, in: Proc. 7th Asian Control Conf., 2009, pp. 105-110.
[22] Xiao, F.; Wang, L., Consensus problems for high-dimensional multi-agent systems, IET control theory appl., 1, 3, 830-837, (2007)
[23] Branicky, M.S., Multiple Lyapunov functions and other analysis tools for switched and hybrid systems, IEEE trans. automat. control, 43, 475-482, (1998) · Zbl 0904.93036
[24] Liberzon, D.; Morse, A.S., Basic problems in stability and design of switched systems, IEEE control mag., 19, 59-70, (1999) · Zbl 1384.93064
[25] Lin, H.; Antsaklis, P.J., Stability and stabilizability of switched linear systems: A survey of recent results, IEEE trans. automat. control, 54, 2, 308-322, (2009) · Zbl 1367.93440
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.