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Consentability and protocol design of multi-agent systems with stochastic switching topology. (English) Zbl 1162.94431
Summary: This paper studies the mean square consentability problem for a network of double-integrator agents with stochastic switching topology. It is proved that in Markov-switching topologies, the network is mean square consentable under linear consensus protocol if and only if the union of graphs in the switching topology set has globally reachable nodes. A necessary and sufficient condition of the mean square consensus is obtained. Finally, an LMI approach to the design of the consensus protocol is presented. Numerical simulations are given to illustrate the results.

MSC:
94C10 Switching theory, application of Boolean algebra; Boolean functions (MSC2010)
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[1] Costa, O.L.V.; Fragoso, M.D., Stability results for discrete-time linear systems with Markovian jumping parameters, Journal of mathematical analysis and applications, 179, 154-178, (1993) · Zbl 0790.93108
[2] Ghaoui, L.E.; Oustry, F.; AitRami, M., A cone complementarity linearization algorithm for static output-feedback and related problems, IEEE transactions on automatic control, 42, 8, 1171-1176, (1997) · Zbl 0887.93017
[3] Hatano, Y.; Mesbahi, M., Agreement over random networks, IEEE transactions on automatic control, 50, 11, 1867-1872, (2005) · Zbl 1365.94482
[4] 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
[5] Lin, Z.Y.; Francis, B.; Maggiore, M., Necessary and sufficient graphical conditions for formation control of unicycles, IEEE transactions on automatic control, 50, 1, 121-127, (2005) · Zbl 1365.93324
[6] Moreau, L., Stability of multiagent systems with time-dependent communication links, IEEE transactions on automatic control, 50, 2, 169-182, (2005) · Zbl 1365.93268
[7] 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
[8] Olfati-Saber, R.; Fax, J.A.; Murray, R.M., Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95, 1, 215-233, (2007) · Zbl 1376.68138
[9] Porfiri, M.; Stilwell, D.J., Consensus seeking over random weighted directed graphs, IEEE transactions on automatic control, 52, 9, 1767-1773, (2007) · Zbl 1366.93330
[10] 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
[11] Ren, W.; Beard, R.W.; Atkins, E.M., Information consensus in multivehicle cooperative control, IEEE control systems magazine, 27, 2, 71-82, (2007)
[12] Ren, W. (2007). Second-order consensus algorithm with extensions to switching topologies and reference models. In Proceedings of the American control conference (pp. 1431-1436)
[13] 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
[14] Tahbaz-Salehi, A.; Jadbabaie, A., A necessary and sufficient condition for consensus over random networks, IEEE transactions on automatic control, 53, 3, 791-795, (2008) · Zbl 1367.90015
[15] Tanner, H.G.; Jadbabaie, A.; Pappas, G.J., Flocking in fixed and switching networks, IEEE transactions on automatic control, 52, 5, 863-868, (2007) · Zbl 1366.93414
[16] Tian, Y.-P.; Liu, C.-L., Consensus of multi-agent systems with diverse input and communication delays, IEEE transactions on automatic control, 53, 9, 2122-2128, (2008) · Zbl 1367.93411
[17] Vicsek, T.; Czirok, 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)
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