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Optimization for a special class of traffic flow models: Combinatorial and continuous approaches
A revisit to the consensus for linearized Vicsek model under joint rooted leadership via a special matrix
1. | Department of Mathematics, Harbin Institute of Technology, Harbin 150001, China |
2. | Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul 151-747 |
References:
[1] |
N. Barabanov, Lyapunov exponent and joint spectral radius: Some known and new results, in Proc. 44th Conf. Decision and Control, Seville, Spain, 2005, 2332-2337.
doi: 10.1109/CDC.2005.1582510. |
[2] |
D. P. Bertsekas and J. N. Tsitsiklis, Comments on "Coordination of groups of mobile autonomous agents using nearest neighbor rules'', IEEE Trans. Automat. Control, 52 (2007), 968-969.
doi: 10.1109/TAC.2007.895885. |
[3] |
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: A graphic approach, SIAM J. Control Optim., 47 (2008), 575-600.
doi: 10.1137/060657005. |
[4] |
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: Vonvergence rates, meansurement delays, and asynchronous events, SIAM J. Control Optim., 47 (2008), 601-623.
doi: 10.1137/060657029. |
[5] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[6] |
R. Diestel, Graph Theory, Graduate Texts in Mathematics, Springer-Verlag, New York, 1997. |
[7] |
L. X. Gao and D. Z. Cheng, Comment on ‘Coordination of groups of mobile agents using nearest neighbor rules', IEEE Trans. Autom. Control, 50 (2005), 1913-1916.
doi: 10.1109/TAC.2005.858635. |
[8] |
S.-Y. Ha, Z. Li, M. Slemrod and X. Xue, Flocking behavior of the Cucker-Smale model under rooted leadership in a large coupling limit, to appear in Quart. Appl. Math. |
[9] |
J. M. Hendrickx, Graphs and Networks for the Analysis of Autonomous Agent Systems, Ph.D Thesis, Université Catholique de Louvain, Department of Mathematical Engineering, February 2008. |
[10] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile agents using nearest neighbor rules, IEEE Trans. Autom. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[11] |
Z. Li, S.-Y. Ha and X. Xue, Emergent phenomena in an ensemble of Cucker-Smale particles under joint rooted leadership, Math. Mod. Meth. Appl. Sci., 24 (2014), 1389-1419.
doi: 10.1142/S0218202514500043. |
[12] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with fixed and switching topologies, SIAM J. Appl. Math., 70 (2010), 3156-3174.
doi: 10.1137/100791774. |
[13] |
Z.-X. Liu and L. Guo, Connectivity and synchronization of Vicsek model, Sci. China Ser. F-Inf. Sci., 51 (2008), 848-858.
doi: 10.1007/s11432-008-0077-2. |
[14] |
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. |
[15] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Schochet, 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. |
[16] |
X. Xue and L. Guo, A kind of nonnegative matrices and its application on the stability of discrete dynamical systems, J. Math. Anal. Appl., 331 (2007), 1113-1121.
doi: 10.1016/j.jmaa.2006.09.053. |
[17] |
X. Xue and Z. Li, Asymptotic stability analysis of a kind of switched positive linear discrete systems, IEEE Trans. Autom. Control, 55 (2010), 2198-2203.
doi: 10.1109/TAC.2010.2052144. |
show all references
References:
[1] |
N. Barabanov, Lyapunov exponent and joint spectral radius: Some known and new results, in Proc. 44th Conf. Decision and Control, Seville, Spain, 2005, 2332-2337.
doi: 10.1109/CDC.2005.1582510. |
[2] |
D. P. Bertsekas and J. N. Tsitsiklis, Comments on "Coordination of groups of mobile autonomous agents using nearest neighbor rules'', IEEE Trans. Automat. Control, 52 (2007), 968-969.
doi: 10.1109/TAC.2007.895885. |
[3] |
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: A graphic approach, SIAM J. Control Optim., 47 (2008), 575-600.
doi: 10.1137/060657005. |
[4] |
M. Cao, A. S. Morse and B. D. O. Anderson, Reaching a consensus in a dynamically changing environment: Vonvergence rates, meansurement delays, and asynchronous events, SIAM J. Control Optim., 47 (2008), 601-623.
doi: 10.1137/060657029. |
[5] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[6] |
R. Diestel, Graph Theory, Graduate Texts in Mathematics, Springer-Verlag, New York, 1997. |
[7] |
L. X. Gao and D. Z. Cheng, Comment on ‘Coordination of groups of mobile agents using nearest neighbor rules', IEEE Trans. Autom. Control, 50 (2005), 1913-1916.
doi: 10.1109/TAC.2005.858635. |
[8] |
S.-Y. Ha, Z. Li, M. Slemrod and X. Xue, Flocking behavior of the Cucker-Smale model under rooted leadership in a large coupling limit, to appear in Quart. Appl. Math. |
[9] |
J. M. Hendrickx, Graphs and Networks for the Analysis of Autonomous Agent Systems, Ph.D Thesis, Université Catholique de Louvain, Department of Mathematical Engineering, February 2008. |
[10] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile agents using nearest neighbor rules, IEEE Trans. Autom. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[11] |
Z. Li, S.-Y. Ha and X. Xue, Emergent phenomena in an ensemble of Cucker-Smale particles under joint rooted leadership, Math. Mod. Meth. Appl. Sci., 24 (2014), 1389-1419.
doi: 10.1142/S0218202514500043. |
[12] |
Z. Li and X. Xue, Cucker-Smale flocking under rooted leadership with fixed and switching topologies, SIAM J. Appl. Math., 70 (2010), 3156-3174.
doi: 10.1137/100791774. |
[13] |
Z.-X. Liu and L. Guo, Connectivity and synchronization of Vicsek model, Sci. China Ser. F-Inf. Sci., 51 (2008), 848-858.
doi: 10.1007/s11432-008-0077-2. |
[14] |
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. |
[15] |
T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Schochet, 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. |
[16] |
X. Xue and L. Guo, A kind of nonnegative matrices and its application on the stability of discrete dynamical systems, J. Math. Anal. Appl., 331 (2007), 1113-1121.
doi: 10.1016/j.jmaa.2006.09.053. |
[17] |
X. Xue and Z. Li, Asymptotic stability analysis of a kind of switched positive linear discrete systems, IEEE Trans. Autom. Control, 55 (2010), 2198-2203.
doi: 10.1109/TAC.2010.2052144. |
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