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Dynamical behavior of networks of non-uniform Timoshenko beams system with boundary time-delay inputs
Consensus and synchronization in discrete-time networks of multi-agents with stochastically switching topologies and time delays
1. | Center for Computational Systems Biology, Laboratory of Mathematics for Nonlinear Sciences, School of Mathematical Sciences, Fudan University, Shanghai, 200433 |
2. | Max Planck Institute for Mathematics in theSciences, Inselstr. 22, 04103 Leipzig, Germany |
References:
[1] |
P.-A. Bliman and G. Ferrari-Trecate, Average consensus problems in networks of agents with delayed communications, Automatica, 44 (2008), 1985-1995.
doi: 10.1016/j.automatica.2007.12.010. |
[2] |
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: A graphical approach, SIAM J. Control Optim., 47 (2008), 575-600.
doi: 10.1137/060657005. |
[3] |
S. Chatterjee and E. Seneta, Towards consensus: Some convergence theorems on repeated averaging, J. Appl. Prob., 14 (1977), 89-97.
doi: 10.2307/3213262. |
[4] |
O. Chilina, "f-Uniform Ergodicity of Markov Chains,'' Supervised Project, Unversity of Toronto, 2006. |
[5] |
M. H. DeGroot, Reaching a consensus, J. Amer. Statist. Assoc., 69 (1974), 118-121.
doi: 10.2307/2285509. |
[6] |
D. V. Dimarogonasa and K. H. Johansson, Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control, Automatica, 46 (2010), 695-700.
doi: 10.1016/j.automatica.2010.01.012. |
[7] |
R. Durrett, "Probability: Theory and Examples," 3rd edition, Belmont, CA: Duxbury Press, 2005. |
[8] |
F. Fagnani and S. Zampieri, Average consensus with packet drop communication, SIAM J. Control Optim., 48 (2009), 102-133.
doi: 10.1137/060676866. |
[9] |
L. Fang, P. J. Antsaklis and A. Tzimas, Asynchronous consensus protocols: Preliminary results, simulations and open questions, Proceedings of the 44th IEEE Conf. Decision and Control, the Europ. Control Conference (2005), 2194-2199. |
[10] |
J. A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formations, IEEE Trans. Autom. Control, 49 (2004), 1465-1476.
doi: 10.1109/TAC.2004.834433. |
[11] |
C. Godsil and G. Royle, "Algebraic Graph Theory," Springer-Verlag, New York, 2001. |
[12] |
J. Hajnal, The ergodic properties of non-homogeneous finite Markov chains, Proc. Camb. Phil. Soc., 52 (1956), 67-77.
doi: 10.1017/S0305004100030991. |
[13] |
J. Hajnal, Weak ergodicity in non-homogeneous Markov chains, Proc. Camb. Phil. Soc., 54 (1958), 233-246.
doi: 10.1017/S0305004100033399. |
[14] |
Y. Hatano and M. Mesbahi, Agreement over random networks, IEEE Trans. Autom. Control, 50 (2005), 1867-1872.
doi: 10.1109/TAC.2005.858670. |
[15] |
R. A. Horn and C. R. Johnson, "Matrix Analysis," Cambridge University Press, 1985. |
[16] |
Y. Kuramoto, "Chemical Oscillations, Waves, And Turbulence," Springer-Verlag, New York, 1984. |
[17] |
J. Lin, A. S. Morse and B. D. O. Anderson, The multi-agent rendezvous problem Part 2: The asynchronous case, SIAM J. Control Optim., 46 (2007), 2120-2147.
doi: 10.1137/040620564. |
[18] |
B. Liu, W. Lu and T. Chen, Consensus in networks of multiagents with switching topologies modeled as adapted stochastic processes, SIAM J. Control Optim., 49 (2011), 227-253.
doi: 10.1137/090745945. |
[19] |
W. Lu, F. M. Atay and J. Jost, Synchronization of discrete-time networks with time-varying couplings, SIAM J. Math. Analys., 39 (2007), 1231-1259.
doi: 10.1137/060657935. |
[20] |
W. Lu, F. M. Atay and J. Jost, Chaos synchronization in networks of coupled maps with time-varying topologies, Eur. Phys. J. B, 63 (2008), 399-406.
doi: 10.1140/epjb/e2008-00023-3. |
[21] |
N. A. Lynch, "Distributed Algorithms," CA: Morgan Kaufmann, San Francisco, 1996. |
[22] |
W. Ni and D. Z. Cheng, Leader-following consensus of multi-agent systems under fixed and switching topologies, Systems & Control Letters, 59 (2010), 209-217.
doi: 10.1016/j.sysconle.2010.01.006. |
[23] |
W. Michiels, C.-I. Morărescu and S.-I. Niculescu, Consensus problems with distributed delays, with application to traffic flow models, SIAM J. Control Optim., 48 (2009), 77-101.
doi: 10.1137/060671425. |
[24] |
L. Moreau, Stability of continuous-time distributed consensus algorithms, 43rd IEEE Conference on Decision and Control, 4 (2004), 3998-4003. |
[25] |
L. Moreau, Stability of multiagent systems with time-dependent communication links, IEEE Trans. Autom. Control, 50 (2005), 169-182.
doi: 10.1109/TAC.2004.841888. |
[26] |
R. Olfati-Saber and J. S. Shamma, Consensus filters for sensor networks and distributed sensor fusion, 44th IEEE Conference on Decision and Control 2005, and 2005 European Control Conference CDC-ECC '05. 6698-6703.
doi: 10.1109/CDC.2005.1583238. |
[27] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233.
doi: 10.1109/JPROC.2006.887293. |
[28] |
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), 1520-1533.
doi: 10.1109/TAC.2004.834113. |
[29] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge University Press, 2001.
doi: 10.1017/CBO9780511755743. |
[30] |
J. Shen, A geometric approach to ergodic non-homogeneous Markov chains, Wavelet Anal. Multi. Meth., LNPAM, 212 (2000), 341-366. |
[31] |
A. Tahbaz-Salehi and A. Jadbabaie, A necessary and sufficient condition for consensus over random networks, IEEE Trans. Autom. Control, 53 (2008), 791-795.
doi: 10.1109/TAC.2008.917743. |
[32] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
[33] |
A. T. Winfree, "The Geometry of Biological Time," Springer Verlag, New York, 1980. |
[34] |
J. Wolfowitz, Products of indecomposable, aperiodic, stochastic matrices, Proceedings of AMS, 14 (1963), 733-737. |
[35] |
C. W. Wu, Synchronization and convergence of linear dynamics in random directed networks, IEEE Trans. Autom. Control, 51 (2006), 1207-1210. |
[36] |
F. Xiao and L. Wang, Consensus protocols for discrete-time multi-agent systems with time-varying delays, Automatica, 44 (2008), 2577-2582. |
[37] |
F. Xiao and L. Wang, Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE Transactions on Automatic Control, 53 (2008), 1804-1816. |
[38] |
Y. Zhang and Y.-P. Tian, Consentability and protocol design of multi-agent systems with stochastic switching topology, Automatica, 45 (2009), 1195-1201. |
show all references
References:
[1] |
P.-A. Bliman and G. Ferrari-Trecate, Average consensus problems in networks of agents with delayed communications, Automatica, 44 (2008), 1985-1995.
doi: 10.1016/j.automatica.2007.12.010. |
[2] |
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: A graphical approach, SIAM J. Control Optim., 47 (2008), 575-600.
doi: 10.1137/060657005. |
[3] |
S. Chatterjee and E. Seneta, Towards consensus: Some convergence theorems on repeated averaging, J. Appl. Prob., 14 (1977), 89-97.
doi: 10.2307/3213262. |
[4] |
O. Chilina, "f-Uniform Ergodicity of Markov Chains,'' Supervised Project, Unversity of Toronto, 2006. |
[5] |
M. H. DeGroot, Reaching a consensus, J. Amer. Statist. Assoc., 69 (1974), 118-121.
doi: 10.2307/2285509. |
[6] |
D. V. Dimarogonasa and K. H. Johansson, Stability analysis for multi-agent systems using the incidence matrix: Quantized communication and formation control, Automatica, 46 (2010), 695-700.
doi: 10.1016/j.automatica.2010.01.012. |
[7] |
R. Durrett, "Probability: Theory and Examples," 3rd edition, Belmont, CA: Duxbury Press, 2005. |
[8] |
F. Fagnani and S. Zampieri, Average consensus with packet drop communication, SIAM J. Control Optim., 48 (2009), 102-133.
doi: 10.1137/060676866. |
[9] |
L. Fang, P. J. Antsaklis and A. Tzimas, Asynchronous consensus protocols: Preliminary results, simulations and open questions, Proceedings of the 44th IEEE Conf. Decision and Control, the Europ. Control Conference (2005), 2194-2199. |
[10] |
J. A. Fax and R. M. Murray, Information flow and cooperative control of vehicle formations, IEEE Trans. Autom. Control, 49 (2004), 1465-1476.
doi: 10.1109/TAC.2004.834433. |
[11] |
C. Godsil and G. Royle, "Algebraic Graph Theory," Springer-Verlag, New York, 2001. |
[12] |
J. Hajnal, The ergodic properties of non-homogeneous finite Markov chains, Proc. Camb. Phil. Soc., 52 (1956), 67-77.
doi: 10.1017/S0305004100030991. |
[13] |
J. Hajnal, Weak ergodicity in non-homogeneous Markov chains, Proc. Camb. Phil. Soc., 54 (1958), 233-246.
doi: 10.1017/S0305004100033399. |
[14] |
Y. Hatano and M. Mesbahi, Agreement over random networks, IEEE Trans. Autom. Control, 50 (2005), 1867-1872.
doi: 10.1109/TAC.2005.858670. |
[15] |
R. A. Horn and C. R. Johnson, "Matrix Analysis," Cambridge University Press, 1985. |
[16] |
Y. Kuramoto, "Chemical Oscillations, Waves, And Turbulence," Springer-Verlag, New York, 1984. |
[17] |
J. Lin, A. S. Morse and B. D. O. Anderson, The multi-agent rendezvous problem Part 2: The asynchronous case, SIAM J. Control Optim., 46 (2007), 2120-2147.
doi: 10.1137/040620564. |
[18] |
B. Liu, W. Lu and T. Chen, Consensus in networks of multiagents with switching topologies modeled as adapted stochastic processes, SIAM J. Control Optim., 49 (2011), 227-253.
doi: 10.1137/090745945. |
[19] |
W. Lu, F. M. Atay and J. Jost, Synchronization of discrete-time networks with time-varying couplings, SIAM J. Math. Analys., 39 (2007), 1231-1259.
doi: 10.1137/060657935. |
[20] |
W. Lu, F. M. Atay and J. Jost, Chaos synchronization in networks of coupled maps with time-varying topologies, Eur. Phys. J. B, 63 (2008), 399-406.
doi: 10.1140/epjb/e2008-00023-3. |
[21] |
N. A. Lynch, "Distributed Algorithms," CA: Morgan Kaufmann, San Francisco, 1996. |
[22] |
W. Ni and D. Z. Cheng, Leader-following consensus of multi-agent systems under fixed and switching topologies, Systems & Control Letters, 59 (2010), 209-217.
doi: 10.1016/j.sysconle.2010.01.006. |
[23] |
W. Michiels, C.-I. Morărescu and S.-I. Niculescu, Consensus problems with distributed delays, with application to traffic flow models, SIAM J. Control Optim., 48 (2009), 77-101.
doi: 10.1137/060671425. |
[24] |
L. Moreau, Stability of continuous-time distributed consensus algorithms, 43rd IEEE Conference on Decision and Control, 4 (2004), 3998-4003. |
[25] |
L. Moreau, Stability of multiagent systems with time-dependent communication links, IEEE Trans. Autom. Control, 50 (2005), 169-182.
doi: 10.1109/TAC.2004.841888. |
[26] |
R. Olfati-Saber and J. S. Shamma, Consensus filters for sensor networks and distributed sensor fusion, 44th IEEE Conference on Decision and Control 2005, and 2005 European Control Conference CDC-ECC '05. 6698-6703.
doi: 10.1109/CDC.2005.1583238. |
[27] |
R. Olfati-Saber, J. A. Fax and R. M. Murray, Consensus and cooperation in networked multi-agent systems, Proceedings of the IEEE, 95 (2007), 215-233.
doi: 10.1109/JPROC.2006.887293. |
[28] |
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), 1520-1533.
doi: 10.1109/TAC.2004.834113. |
[29] |
A. Pikovsky, M. Rosenblum and J. Kurths, "Synchronization: A Universal Concept in Nonlinear Sciences," Cambridge University Press, 2001.
doi: 10.1017/CBO9780511755743. |
[30] |
J. Shen, A geometric approach to ergodic non-homogeneous Markov chains, Wavelet Anal. Multi. Meth., LNPAM, 212 (2000), 341-366. |
[31] |
A. Tahbaz-Salehi and A. Jadbabaie, A necessary and sufficient condition for consensus over random networks, IEEE Trans. Autom. Control, 53 (2008), 791-795.
doi: 10.1109/TAC.2008.917743. |
[32] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles, Phys. Rev. Lett., 75 (1995), 1226-1229.
doi: 10.1103/PhysRevLett.75.1226. |
[33] |
A. T. Winfree, "The Geometry of Biological Time," Springer Verlag, New York, 1980. |
[34] |
J. Wolfowitz, Products of indecomposable, aperiodic, stochastic matrices, Proceedings of AMS, 14 (1963), 733-737. |
[35] |
C. W. Wu, Synchronization and convergence of linear dynamics in random directed networks, IEEE Trans. Autom. Control, 51 (2006), 1207-1210. |
[36] |
F. Xiao and L. Wang, Consensus protocols for discrete-time multi-agent systems with time-varying delays, Automatica, 44 (2008), 2577-2582. |
[37] |
F. Xiao and L. Wang, Asynchronous consensus in continuous-time multi-agent systems with switching topology and time-varying delays, IEEE Transactions on Automatic Control, 53 (2008), 1804-1816. |
[38] |
Y. Zhang and Y.-P. Tian, Consentability and protocol design of multi-agent systems with stochastic switching topology, Automatica, 45 (2009), 1195-1201. |
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