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Consensus of discrete-time linear multi-agent systems with observer-type protocols
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 |
$\delta$ ($0<\delta<1$) as its consensus region. Finally, the consensus algorithms are applied to solve formation control problems of multi-agent systems.
References:
[1] |
D. Bauso, L. Giarré and R. Pesenti, Consensus for netowrks with unknown but bounded disturbances,, SIAM J. Control Optim., 48 (2009), 1756.
doi: 10.1137/060678786. |
[2] |
S. Bowong and J. L. Dimi, Adaptive synchronization of a class of uncertain chaotic systems,, Discret. Contin. Dyn. Syst., 9 (2008), 235.
|
[3] |
J. Cortés, Distributed algorithms for reaching consensus on general functions,, Automatica, 44 (2008), 726.
doi: 10.1016/j.automatica.2007.07.022. |
[4] |
Z. S. Duan, G. R. Chen and L. Huang, Synchronization of weighted networks and complex synchronized regions,, Phys. Lett. A, 372 (2008), 3741.
doi: 10.1016/j.physleta.2008.02.056. |
[5] |
Z. S. Duan, G. R. Chen and L. Huang, Disconnected synchronized regions of complex dynamical networks,, IEEE Trans. Autom. Control, 54 (2009), 845.
doi: 10.1109/TAC.2008.2009690. |
[6] |
J. A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formations,, IEEE Trans. Automat. Control, 49 (2004), 1465.
doi: 10.1109/TAC.2004.834433. |
[7] |
P. Frasca, R. Carli, F. Pagnani and S. Zampieri, Average consensus on networks with quantized communication,, Int. J. Robust Nonlinear Control, 19 (2008), 1787.
doi: 10.1002/rnc.1396. |
[8] |
Y. Hong, J. Hu and L. Gao, Tracking control for multi-agent consensus with an active leader and variable topology,, Automatica, 42 (2006), 1177.
doi: 10.1016/j.automatica.2006.02.013. |
[9] |
Y. Hong, G. R. Chen and L. Bushnell, Distributed observers design for leader-following control of multi-agent,, Automatica, 44 (2008), 846.
doi: 10.1016/j.automatica.2007.07.004. |
[10] |
R. Horn and C. Johnson, "Matrix Analysis,", Cambridge Univ. Press, (1985).
|
[11] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonous agents using neareast neighbor rules,, IEEE Trans. Autom. Control, 48 (2003), 988.
doi: 10.1109/TAC.2003.812781. |
[12] |
T. Katayama, On the matrix Riccati equation for linear systems with a random gain,, IEEE Trans. Autom. Control, 21 (1976), 770.
doi: 10.1109/TAC.1976.1101325. |
[13] |
G. Lafferriere, A. Williams, J. Caughman and J. J. P. Veerman, Decentralized control of vehicle formations,, Syst. Control Lett., 54 (2005), 899.
doi: 10.1016/j.sysconle.2005.02.004. |
[14] |
Z. K. Li, Z. S. Duan and L. Huang, $H_\infty$ control of networked multi-agent systems,, J. Syst. Sci. Complex., 22 (2009), 35.
doi: 10.1007/s11424-009-9145-y. |
[15] |
Z. K. Li, Z. S. Duan, G. R. Chen and L. Huang, Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint,, IEEE Trans. Circuits Syst. I-Regul. Pap., 51 (2010), 213.
|
[16] |
P. Lin, Y. M. Jia and L. Li, Distributed robust $H_\infty$ consensus control in directed networks of agents with time-delay,, Syst. Control Lett., 57 (2008), 643.
doi: 10.1016/j.sysconle.2008.01.002. |
[17] |
P. Lin and Y. M. Jia, Further results on decentralised coordination in networks of agents with second-order dynamics,, IET Contr. Theory Appl., 3 (2009), 957.
doi: 10.1049/iet-cta.2008.0263. |
[18] |
C. Liu, Z. S. Duan, G. R. Chen and L. Huang, Analyzing and controlling the network synchronization regions,, Physica A, 386 (2007), 531.
doi: 10.1016/j.physa.2007.08.006. |
[19] |
C. Q. Ma and J. F. Zhang, Necessary and sufficient conditions for consensusability of linear multi-agent systems,, IEEE Trans. Autom. Control, 55 (2010), 1263.
doi: 10.1109/TAC.2010.2042764. |
[20] |
K. Ogata, "Modern Control Engineering," 3rd, edition, (1996). Google Scholar |
[21] |
R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays,, IEEE Trans. Autom. Control, 49 (2004), 1520.
doi: 10.1109/TAC.2004.834113. |
[22] |
R. Olfati-Saber, Flocking for multi-agent dynamic systems: Algorithms and theory,, IEEE Trans. Autom. Control, 51 (2006), 401.
doi: 10.1109/TAC.2005.864190. |
[23] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems,, Pro. IEEE, 97 (2007), 215.
doi: 10.1109/JPROC.2006.887293. |
[24] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems,, Phys. Rev. Lett., 80 (1998), 2109.
doi: 10.1103/PhysRevLett.80.2109. |
[25] |
W. Ren and R. W. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topogies,, IEEE Trans. Autom. Control, 50 (2005), 655.
doi: 10.1109/TAC.2005.846556. |
[26] |
W. Ren, R. W. Beard and E. M. Atkins, Information consensus in multivehicle cooperative control,, IEEE Control Syst. Mag., 27 (2007), 71.
doi: 10.1109/MCS.2007.338264. |
[27] |
W. Ren, K. L. Moore and Y. Q. Chen, High-order and model reference consensus algorithms in cooperative control of multi-vehicle systems,, J. Dyn. Syst. Meas. Control-Trans. ASME, 129 (2007), 678. Google Scholar |
[28] |
W. Ren, On consensus algorithms for double-integrator dynamics,, IEEE Trans. Autom. Control, 53 (2008), 1503.
|
[29] |
W. Ren and N. Sorensen, Distributed coordination architecture for multi-robot formation control,, Robot. Auton. Syst., 56 (2008), 324.
doi: 10.1016/j.robot.2007.08.005. |
[30] |
A. Rahmani, M. Ji, M. Mesbahi and M. Egerstedt, Controllability of multi-agent systems from a graph-theorectic perspective,, SIAM J. Control Optim., 48 (2009), 162.
doi: 10.1137/060674909. |
[31] |
L. Scardavi and S. Sepulchre, Synchronization in networks of identical linear systems,, Automatica, 45 (2009), 2557.
doi: 10.1016/j.automatica.2009.07.006. |
[32] |
L. Schenato, B. Sinopoli, M. Franceschetti, K. Poolla, M. I. Jordan and S. S. Sastry, Foundations of control and estimation over lossy networks, Proc., IEEE, 95 (2007), 163.
doi: 10.1109/JPROC.2006.887306. |
[33] |
J. H. Seo, H. Shim and J. Back, Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach,, Automatica, 45 (2009), 2659.
doi: 10.1016/j.automatica.2009.07.022. |
[34] |
B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan and S. S. Sastry, Kalman filtering with intermittent observations,, IEEE Trans. Autom. Control, 49 (2004), 1453.
doi: 10.1109/TAC.2004.834121. |
[35] |
Y. G. Sun and W. Long, Consensus problems in networks of agents with double-integrator dynamics and time-varying delays,, Int. J. Control, 82 (2009), 1937.
doi: 10.1080/00207170902838269. |
[36] |
R. S. Smith and F. Y. Hadaegh, Control of deep-space formation-flying spacecraft; Relative sensing and switched information,, J. Guid. Control Dyn., 28 (2005), 106.
doi: 10.2514/1.6165. |
[37] |
H. S. Su, X. F. Wang and Z. L. Lin, Flocking of multi-agents with a virtual leader,, IEEE Trans. Autom. Control, 54 (2009), 293.
doi: 10.1109/TAC.2008.2010897. |
[38] |
H. G. Tanner, A. Jadbabaie and G. J. Pappas, Flocking in fixed and switching networks,, IEEE Trans. Autom. Control, 52 (2007), 863.
doi: 10.1109/TAC.2007.895948. |
[39] |
Y. P. Tian and C. L. Liu, Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations,, Automatica, 45 (2009), 1347.
doi: 10.1016/j.automatica.2009.01.009. |
[40] |
S. E. Tuna, Synchronizing linear systems via partial-state coupling,, Automatica, 44 (2008), 2179.
doi: 10.1016/j.automatica.2008.01.004. |
[41] |
S. E. Tuna, Conditions for synchronizability in arrays of coupled linear systems,, IEEE Trans. Autom. Control, 54 (2009), 2416.
doi: 10.1109/TAC.2009.2029296. |
[42] |
T. Vicsek, A. Cziroók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transitions in a system of self-driven particles,, Phys. Rev. Lett., 75 (1995), 1226.
doi: 10.1103/PhysRevLett.75.1226. |
[43] |
J. H. Wang, D. Z. Cheng and X. M. Hu, Consensus of multi-agent linear dynamic systems,, Asian J. Control, 10 (2008), 144.
doi: 10.1002/asjc.15. |
[44] |
G. Xie and L. Wang, Consensus control for a class of networks of dynamic agents,, Int. J. Robust Nonlinear Control, 17 (2007), 941.
doi: 10.1002/rnc.1144. |
[45] |
R. Yamapi and R. S. Mackay, Stability of synchronization in a shift-invariant ring of mutually coupled oscillators,, Discret. Contin. Dyn. Syst., 10 (2008), 973.
doi: 10.3934/dcdsb.2008.10.973. |
[46] |
H. T. Zhang, M. Z. Q. Chen, T. Zhou and G. B. Stan, Ultrafast consensus via predictive mechanisms,, Europhysics Letters, 83 (2008).
doi: 10.1209/0295-5075/83/40003. |
[47] |
K. M. Zhou and J. C. Doyle, "Essentials of Robust Control,", Prentice-Hall, (1998). Google Scholar |
show all references
References:
[1] |
D. Bauso, L. Giarré and R. Pesenti, Consensus for netowrks with unknown but bounded disturbances,, SIAM J. Control Optim., 48 (2009), 1756.
doi: 10.1137/060678786. |
[2] |
S. Bowong and J. L. Dimi, Adaptive synchronization of a class of uncertain chaotic systems,, Discret. Contin. Dyn. Syst., 9 (2008), 235.
|
[3] |
J. Cortés, Distributed algorithms for reaching consensus on general functions,, Automatica, 44 (2008), 726.
doi: 10.1016/j.automatica.2007.07.022. |
[4] |
Z. S. Duan, G. R. Chen and L. Huang, Synchronization of weighted networks and complex synchronized regions,, Phys. Lett. A, 372 (2008), 3741.
doi: 10.1016/j.physleta.2008.02.056. |
[5] |
Z. S. Duan, G. R. Chen and L. Huang, Disconnected synchronized regions of complex dynamical networks,, IEEE Trans. Autom. Control, 54 (2009), 845.
doi: 10.1109/TAC.2008.2009690. |
[6] |
J. A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formations,, IEEE Trans. Automat. Control, 49 (2004), 1465.
doi: 10.1109/TAC.2004.834433. |
[7] |
P. Frasca, R. Carli, F. Pagnani and S. Zampieri, Average consensus on networks with quantized communication,, Int. J. Robust Nonlinear Control, 19 (2008), 1787.
doi: 10.1002/rnc.1396. |
[8] |
Y. Hong, J. Hu and L. Gao, Tracking control for multi-agent consensus with an active leader and variable topology,, Automatica, 42 (2006), 1177.
doi: 10.1016/j.automatica.2006.02.013. |
[9] |
Y. Hong, G. R. Chen and L. Bushnell, Distributed observers design for leader-following control of multi-agent,, Automatica, 44 (2008), 846.
doi: 10.1016/j.automatica.2007.07.004. |
[10] |
R. Horn and C. Johnson, "Matrix Analysis,", Cambridge Univ. Press, (1985).
|
[11] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonous agents using neareast neighbor rules,, IEEE Trans. Autom. Control, 48 (2003), 988.
doi: 10.1109/TAC.2003.812781. |
[12] |
T. Katayama, On the matrix Riccati equation for linear systems with a random gain,, IEEE Trans. Autom. Control, 21 (1976), 770.
doi: 10.1109/TAC.1976.1101325. |
[13] |
G. Lafferriere, A. Williams, J. Caughman and J. J. P. Veerman, Decentralized control of vehicle formations,, Syst. Control Lett., 54 (2005), 899.
doi: 10.1016/j.sysconle.2005.02.004. |
[14] |
Z. K. Li, Z. S. Duan and L. Huang, $H_\infty$ control of networked multi-agent systems,, J. Syst. Sci. Complex., 22 (2009), 35.
doi: 10.1007/s11424-009-9145-y. |
[15] |
Z. K. Li, Z. S. Duan, G. R. Chen and L. Huang, Consensus of multiagent systems and synchronization of complex networks: A unified viewpoint,, IEEE Trans. Circuits Syst. I-Regul. Pap., 51 (2010), 213.
|
[16] |
P. Lin, Y. M. Jia and L. Li, Distributed robust $H_\infty$ consensus control in directed networks of agents with time-delay,, Syst. Control Lett., 57 (2008), 643.
doi: 10.1016/j.sysconle.2008.01.002. |
[17] |
P. Lin and Y. M. Jia, Further results on decentralised coordination in networks of agents with second-order dynamics,, IET Contr. Theory Appl., 3 (2009), 957.
doi: 10.1049/iet-cta.2008.0263. |
[18] |
C. Liu, Z. S. Duan, G. R. Chen and L. Huang, Analyzing and controlling the network synchronization regions,, Physica A, 386 (2007), 531.
doi: 10.1016/j.physa.2007.08.006. |
[19] |
C. Q. Ma and J. F. Zhang, Necessary and sufficient conditions for consensusability of linear multi-agent systems,, IEEE Trans. Autom. Control, 55 (2010), 1263.
doi: 10.1109/TAC.2010.2042764. |
[20] |
K. Ogata, "Modern Control Engineering," 3rd, edition, (1996). Google Scholar |
[21] |
R. Olfati-Saber and R. M. Murray, Consensus problems in networks of agents with switching topology and time-delays,, IEEE Trans. Autom. Control, 49 (2004), 1520.
doi: 10.1109/TAC.2004.834113. |
[22] |
R. Olfati-Saber, Flocking for multi-agent dynamic systems: Algorithms and theory,, IEEE Trans. Autom. Control, 51 (2006), 401.
doi: 10.1109/TAC.2005.864190. |
[23] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems,, Pro. IEEE, 97 (2007), 215.
doi: 10.1109/JPROC.2006.887293. |
[24] |
L. M. Pecora and T. L. Carroll, Master stability functions for synchronized coupled systems,, Phys. Rev. Lett., 80 (1998), 2109.
doi: 10.1103/PhysRevLett.80.2109. |
[25] |
W. Ren and R. W. Beard, Consensus seeking in multiagent systems under dynamically changing interaction topogies,, IEEE Trans. Autom. Control, 50 (2005), 655.
doi: 10.1109/TAC.2005.846556. |
[26] |
W. Ren, R. W. Beard and E. M. Atkins, Information consensus in multivehicle cooperative control,, IEEE Control Syst. Mag., 27 (2007), 71.
doi: 10.1109/MCS.2007.338264. |
[27] |
W. Ren, K. L. Moore and Y. Q. Chen, High-order and model reference consensus algorithms in cooperative control of multi-vehicle systems,, J. Dyn. Syst. Meas. Control-Trans. ASME, 129 (2007), 678. Google Scholar |
[28] |
W. Ren, On consensus algorithms for double-integrator dynamics,, IEEE Trans. Autom. Control, 53 (2008), 1503.
|
[29] |
W. Ren and N. Sorensen, Distributed coordination architecture for multi-robot formation control,, Robot. Auton. Syst., 56 (2008), 324.
doi: 10.1016/j.robot.2007.08.005. |
[30] |
A. Rahmani, M. Ji, M. Mesbahi and M. Egerstedt, Controllability of multi-agent systems from a graph-theorectic perspective,, SIAM J. Control Optim., 48 (2009), 162.
doi: 10.1137/060674909. |
[31] |
L. Scardavi and S. Sepulchre, Synchronization in networks of identical linear systems,, Automatica, 45 (2009), 2557.
doi: 10.1016/j.automatica.2009.07.006. |
[32] |
L. Schenato, B. Sinopoli, M. Franceschetti, K. Poolla, M. I. Jordan and S. S. Sastry, Foundations of control and estimation over lossy networks, Proc., IEEE, 95 (2007), 163.
doi: 10.1109/JPROC.2006.887306. |
[33] |
J. H. Seo, H. Shim and J. Back, Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach,, Automatica, 45 (2009), 2659.
doi: 10.1016/j.automatica.2009.07.022. |
[34] |
B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan and S. S. Sastry, Kalman filtering with intermittent observations,, IEEE Trans. Autom. Control, 49 (2004), 1453.
doi: 10.1109/TAC.2004.834121. |
[35] |
Y. G. Sun and W. Long, Consensus problems in networks of agents with double-integrator dynamics and time-varying delays,, Int. J. Control, 82 (2009), 1937.
doi: 10.1080/00207170902838269. |
[36] |
R. S. Smith and F. Y. Hadaegh, Control of deep-space formation-flying spacecraft; Relative sensing and switched information,, J. Guid. Control Dyn., 28 (2005), 106.
doi: 10.2514/1.6165. |
[37] |
H. S. Su, X. F. Wang and Z. L. Lin, Flocking of multi-agents with a virtual leader,, IEEE Trans. Autom. Control, 54 (2009), 293.
doi: 10.1109/TAC.2008.2010897. |
[38] |
H. G. Tanner, A. Jadbabaie and G. J. Pappas, Flocking in fixed and switching networks,, IEEE Trans. Autom. Control, 52 (2007), 863.
doi: 10.1109/TAC.2007.895948. |
[39] |
Y. P. Tian and C. L. Liu, Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations,, Automatica, 45 (2009), 1347.
doi: 10.1016/j.automatica.2009.01.009. |
[40] |
S. E. Tuna, Synchronizing linear systems via partial-state coupling,, Automatica, 44 (2008), 2179.
doi: 10.1016/j.automatica.2008.01.004. |
[41] |
S. E. Tuna, Conditions for synchronizability in arrays of coupled linear systems,, IEEE Trans. Autom. Control, 54 (2009), 2416.
doi: 10.1109/TAC.2009.2029296. |
[42] |
T. Vicsek, A. Cziroók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transitions in a system of self-driven particles,, Phys. Rev. Lett., 75 (1995), 1226.
doi: 10.1103/PhysRevLett.75.1226. |
[43] |
J. H. Wang, D. Z. Cheng and X. M. Hu, Consensus of multi-agent linear dynamic systems,, Asian J. Control, 10 (2008), 144.
doi: 10.1002/asjc.15. |
[44] |
G. Xie and L. Wang, Consensus control for a class of networks of dynamic agents,, Int. J. Robust Nonlinear Control, 17 (2007), 941.
doi: 10.1002/rnc.1144. |
[45] |
R. Yamapi and R. S. Mackay, Stability of synchronization in a shift-invariant ring of mutually coupled oscillators,, Discret. Contin. Dyn. Syst., 10 (2008), 973.
doi: 10.3934/dcdsb.2008.10.973. |
[46] |
H. T. Zhang, M. Z. Q. Chen, T. Zhou and G. B. Stan, Ultrafast consensus via predictive mechanisms,, Europhysics Letters, 83 (2008).
doi: 10.1209/0295-5075/83/40003. |
[47] |
K. M. Zhou and J. C. Doyle, "Essentials of Robust Control,", Prentice-Hall, (1998). Google Scholar |
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