American Institute of Mathematical Sciences

Advanced
September  2011, 16(2): 489-505. doi: 10.3934/dcdsb.2011.16.489

Consensus of discrete-time linear multi-agent systems with observer-type protocols

Zhongkui Li 1, , Zhisheng Duan 2, and  Guanrong Chen 3,

1. 

School of Automation, Beijing Institute of Technology, Beijing 100081, P. R., China
2. 

State Key Lab for Turbulence and Complex Systems, Department of Mechanics and Aerospace Engineering, College of Engineering, Peking University, Beijing 100871, P. R., China
3. 

Department of Electronic Engineering, City University of Hong Kong, Hong Kong

Received  December 2009 Revised  October 2010 Published  June 2011

This paper concerns the consensus of discrete-time multi-agent systems with linear or linearized dynamics. An observer-type protocol based on the relative outputs of neighboring agents is proposed. The consensus of such a multi-agent system with a directed communication topology can be cast into the stability of a set of matrices with the same low dimension as that of a single agent. The notion of discrete-time consensus region is then introduced and analyzed. For neurally stable agents, it is shown that there exists an observer-type protocol having a bounded consensus region in the form of an open unit disk, provided that each agent is stabilizable and detectable. An algorithm is further presented to construct a protocol to achieve consensus with respect to all the communication topologies containing a spanning tree. Moreover, for the case where the agents have no poles outside the unit circle, an algorithm is proposed to construct a protocol having an origin-centered disk of radius
$\delta$ ($0<\delta<1$) as its consensus region. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.
Keywords: discrete-time linear system, multi-agent system, formation control., consensus region, observer-type protocol, Consensus.
Mathematics Subject Classification: Primary: 93A14, 93C55; Secondary: 93C0.
Citation: Zhongkui Li, Zhisheng Duan, Guanrong Chen. Consensus of discrete-time linear multi-agent systems with observer-type protocols. Discrete & Continuous Dynamical Systems - B, 2011, 16 (2) : 489-505. doi: 10.3934/dcdsb.2011.16.489
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show all references

References:
[1]

SIAM J. Control Optim., 48 (2009), 1756-1770. doi: 10.1137/060678786.  Google Scholar

[2]

Discret. Contin. Dyn. Syst., 9 (2008), 235-248.  Google Scholar

[3]

Automatica, 44 (2008), 726-737. doi: 10.1016/j.automatica.2007.07.022.  Google Scholar

[4]

Phys. Lett. A, 372 (2008), 3741-3751. doi: 10.1016/j.physleta.2008.02.056.  Google Scholar

[5]

IEEE Trans. Autom. Control, 54 (2009), 845-849. doi: 10.1109/TAC.2008.2009690.  Google Scholar

[6]

IEEE Trans. Automat. Control, 49 (2004), 1465-1476. doi: 10.1109/TAC.2004.834433.  Google Scholar

[7]

Int. J. Robust Nonlinear Control, 19 (2008), 1787-1816. doi: 10.1002/rnc.1396.  Google Scholar

[8]

Automatica, 42 (2006), 1177-1182. doi: 10.1016/j.automatica.2006.02.013.  Google Scholar

[9]

Automatica, 44 (2008), 846-850. doi: 10.1016/j.automatica.2007.07.004.  Google Scholar

[10]

Cambridge Univ. Press, New York, 1985.  Google Scholar

[11]

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[12]

IEEE Trans. Autom. Control, 21 (1976), 770-771. doi: 10.1109/TAC.1976.1101325.  Google Scholar

[13]

Syst. Control Lett., 54 (2005), 899-910. doi: 10.1016/j.sysconle.2005.02.004.  Google Scholar

[14]

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[15]

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[16]

Syst. Control Lett., 57 (2008), 643-653. doi: 10.1016/j.sysconle.2008.01.002.  Google Scholar

[17]

IET Contr. Theory Appl., 3 (2009), 957-970. doi: 10.1049/iet-cta.2008.0263.  Google Scholar

[18]

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[19]

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[20]

edition, Prentice Hall: Englewood Cliffs, 1996. Google Scholar

[21]

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[22]

IEEE Trans. Autom. Control, 51 (2006), 401-420. doi: 10.1109/TAC.2005.864190.  Google Scholar

[23]

Pro. IEEE, 97 (2007), 215-233. doi: 10.1109/JPROC.2006.887293.  Google Scholar

[24]

Phys. Rev. Lett., 80 (1998), 2109-2112. doi: 10.1103/PhysRevLett.80.2109.  Google Scholar

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[30]

SIAM J. Control Optim., 48 (2009), 162-186. doi: 10.1137/060674909.  Google Scholar

[31]

Automatica, 45 (2009), 2557-2562. doi: 10.1016/j.automatica.2009.07.006.  Google Scholar

[32]

IEEE, 95 (2007), 163-187. doi: 10.1109/JPROC.2006.887306.  Google Scholar

[33]

Automatica, 45 (2009), 2659-2664. doi: 10.1016/j.automatica.2009.07.022.  Google Scholar

[34]

IEEE Trans. Autom. Control, 49 (2004), 1453-1464. doi: 10.1109/TAC.2004.834121.  Google Scholar

[35]

Int. J. Control, 82 (2009), 1937-1945. doi: 10.1080/00207170902838269.  Google Scholar

[36]

J. Guid. Control Dyn., 28 (2005), 106-114. doi: 10.2514/1.6165.  Google Scholar

[37]

IEEE Trans. Autom. Control, 54 (2009), 293-307. doi: 10.1109/TAC.2008.2010897.  Google Scholar

[38]

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[39]

Automatica, 45 (2009), 1347-1353. doi: 10.1016/j.automatica.2009.01.009.  Google Scholar

[40]

Automatica, 44 (2008), 2179-2184. doi: 10.1016/j.automatica.2008.01.004.  Google Scholar

[41]

IEEE Trans. Autom. Control, 54 (2009), 2416-2420. doi: 10.1109/TAC.2009.2029296.  Google Scholar

[42]

Phys. Rev. Lett., 75 (1995), 1226-1229. doi: 10.1103/PhysRevLett.75.1226.  Google Scholar

[43]

Asian J. Control, 10 (2008), 144-155. doi: 10.1002/asjc.15.  Google Scholar

[44]

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Discret. Contin. Dyn. Syst., 10 (2008), 973-996. doi: 10.3934/dcdsb.2008.10.973.  Google Scholar

[46]

Europhysics Letters, 83 (2008), 40003. doi: 10.1209/0295-5075/83/40003.  Google Scholar

[47]

Prentice-Hall, Englewood Cliffs, 1998. Google Scholar

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