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On consensus speed of multi-agent systems with double-integrator dynamics. (English) Zbl 1201.93011

Summary: The performance of multi-agent systems is an important issue. In this paper, it is focused on consensus speed for multi-agent systems with double-integrator dynamics and fixed undirected graphes under a kind of consensus protocols. It is revealed that, under some conditions, the maximum consensus speed is determined by the largest and the smallest nonzero eigenvalues of the Laplacian matrix of the undirected connected graph. Based on the mentioned results, arbitrary desired consensus speed can be achieved by choosing suitable feedback gains. Numerical simulations are given to illustrate the main results.

MSC:

93A14 Decentralized systems
93C15 Control/observation systems governed by ordinary differential equations
34K35 Control problems for functional-differential equations
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[1] Wang, P.K.C.; Hadaegh, F.Y., Coordination and control of multiple microspacecraft moving in formation, J. astronaut. sci., 44, 3, 315-355, (1994)
[2] Balch, T.; Arkin, R.C., Behavior-based formation control for multirobot terms, IEEE trans. robot. automat., 14, 6, 926-939, (1998)
[3] Hu, X., Formation control with virtual leaders and reduced communications, IEEE trans. robot. automat., 17, 6, 947-951, (2001)
[4] Fax, A.; Murray, R.M., Information flow and cooperative control of vehicle formations, IEEE trans. automat. control, 49, 9, 1465-1476, (2004) · Zbl 1365.90056
[5] Toner, J.; Tu, Y., Flocks, herds, and schools: a quantitative theory of flocking, Phys. rev. W, 58, 4, 4828-4858, (1998)
[6] Olfati-Saber, R.; Murray, R.M., Flocking for multi-agent dynamic systems: algorithms and theory, IEEE trans. automat. control, 51, 3, 401-420, (2006) · Zbl 1366.93391
[7] Vicsek, T.; Czirok, A.; Ben-Jacob, E., Novel type of phase transitions in a system of self-driven particles, Phys. rev. lett., 75, 6, 1226-1229, (1995)
[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] R.O. Saber, R.M. Murray, Consensus protocols for networks of dynamic agents, in: Proc. Amer. Contr. Conf., 2003, pp. 951-956.
[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] Ren, W.; Beard, R.W., Consensus seeking in multi-agent systems under dynamically changing interaction topologies, IEEE trans. automat. control, 50, 5, 655-661, (2005) · Zbl 1365.93302
[12] Lin, Z.Y.; Francis, B.; Maggiore, M., Necessary and sufficient graphical condition for formation control of unicycles, IEEE trans. automat. control, 50, 1, 121-127, (2005) · Zbl 1365.93324
[13] 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
[14] 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
[15] P. Lin, Y. Jia, J. Du, S. Yuan, Distributed consensus control for second-order agents with fixed topology and time-delay, in: Proc. 26th Chinese Contr. Conf., Zhangjiajie, Hunan, PR China, 2007, pp. 577-581.
[16] Zhang, Y.; Tian, Y.-P., Consentability and protocol design of multi-agent systems with stochastic switching topology, Automatica, 45, 5, 1195-1201, (2009) · Zbl 1162.94431
[17] Ren, W., Synchronization of coupled harmonic oscillators with local interaction, Automatica, 44, 12, 3195-3200, (2008) · Zbl 1153.93421
[18] Ren, We., On consensus algorithms for double-integrator dynamics, IEEE trans. automat. control, 53, 6, 1503-1509, (2008) · Zbl 1367.93567
[19] Zhu, J.; Tian, Y.-P.; Kuang, J., On the general consensus protocol of multi-agent systems with double-integrator dynamics, Linear algebra appl., 431, 5-7, 701-715, (2009) · Zbl 1165.93022
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