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A conditional, collision-avoiding, model for swarming
1. | Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon Tong, Hong Kong, China |
2. | Department of Mathematics, Harbin Institute of Technology, Harbin, 150001, China |
References:
[1] |
J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM. J. Math. Anal., 42 (2010), 218-236.
doi: 10.1137/090757290. |
[2] |
Y. Chuang, Y. Huang, M. D'Orsogna and A. Bertozzi, Multi-vehicle flocking: Scalability of cooperative control algorithms using pairwise potentials, IEEE International Conference on Robotics and Automation, (2007), 2292-2299.
doi: 10.1109/ROBOT.2007.363661. |
[3] |
E. Cristiani, P. Frasca and B. Piccoli, Effects of anisotropic interactions on the structure of animal groups, J. Math. Biol., 62 (2011), 569-588.
doi: 10.1007/s00285-010-0347-7. |
[4] |
F. Cucker and J.-G. Dong, A general collision-avoiding flocking framework, IEEE Trans. Autom. Control, 56 (2011), 1124-1129.
doi: 10.1109/TAC.2011.2107113. |
[5] |
F. Cucker and C. Huepe, Flocking with informed agents, Mathematics in Action, 1 (2008), 1-25.
doi: 10.5802/msia.1. |
[6] |
F. Cucker and E. Mordecki, Flocking in noisy environments, J. Math. Pures Appl., 89 (2008), 278-296.
doi: 10.1016/j.matpur.2007.12.002. |
[7] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Autom. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[8] |
F. Dalmao and E. Mordecki, Cucker-Smale flocking under hierarchical leadership and random interactions, SIAM. J. App. Math., 71 (2011), 1307-1316.
doi: 10.1137/100785910. |
[9] |
V. Gazi and K. M. Passino, Stability analysis of swarms, IEEE Trans. Autom. Control, 48 (2003), 692-697.
doi: 10.1109/TAC.2003.809765. |
[10] |
V. Gazi and K. M. Passino, Stability analysis of social foraging swarms, IEEE Trans. Syst., Man, Cybern. B, 34 (2004), 539-557.
doi: 10.1109/TSMCB.2003.817077. |
[11] |
V. Gazi and K. M. Passino, A class of attractions/repulsion functions for stable swarm aggregations, Int. J. Control, 77 (2004), 1567-1579.
doi: 10.1080/00207170412331330021. |
[12] |
S.-Y. Ha, T.-Y. Ha and J.-G. Kim, Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings, IEEE Trans. Autom. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[13] |
S.-Y. Ha, K. Lee and D. Levy, Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system, Commun. Math. Sci., 7 (2009), 453-469. |
[14] |
S.-Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic descriptions of flocking, Kinetic and Related Models, 1 (2008), 415-435.
doi: 10.3934/krm.2008.1.415. |
[15] |
M. Hirsch and S. Smale, "Differential Equations, Dynamical Systems, and Linear Algebra," 60 of Pure and Applied Mathematics. Academic Press, 1974. |
[16] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. on Autom. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[17] |
J. Kang, S.Y. Ha, E. Jeong and K. K. Kang, How do cultural classes emerge from assimilation and distinction? An extension of the Cucker-Smale flocking model, To Appear in J. Mathematical Sociology. |
[18] |
H. K. Khalil, "Nonlinear Systems," 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 2002. |
[19] |
N. Leonard and E. Fiorelli, Virtual leaders, artificial potentials and coordinated control of groups, Proc. 40th IEEE Conf. Decision Contr., (2001), 2968-2973. |
[20] |
W. Li, Stability analysis of swarms with general topology, IEEE Trans. Syst., Man, Cybern. B, 38 (2008), 1084-1097. |
[21] |
L. Perea, P. Elosegui and G. Gómez, Extension of the Cucker-Smale control law to space flight formations, Journal of Guidance, Control, and Dynamics, 32 (2009), 526-536.
doi: 10.2514/1.36269. |
[22] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math, 68 (2007), 694-719.
doi: 10.1137/060673254. |
[23] |
J. J. E. Slotine and W. Li, "Applied Nonlinear Control," Englewood Cliffs, NJ: Prentice-Hall, 1991. |
[24] |
T. Vicsek and A. Zafeiris, Collective motion, Physics Reports, 517 (2012), 71-140.
doi: 10.1016/j.physrep.2012.03.004. |
show all references
References:
[1] |
J. A. Carrillo, M. Fornasier, J. Rosado and G. Toscani, Asymptotic flocking dynamics for the kinetic Cucker-Smale model, SIAM. J. Math. Anal., 42 (2010), 218-236.
doi: 10.1137/090757290. |
[2] |
Y. Chuang, Y. Huang, M. D'Orsogna and A. Bertozzi, Multi-vehicle flocking: Scalability of cooperative control algorithms using pairwise potentials, IEEE International Conference on Robotics and Automation, (2007), 2292-2299.
doi: 10.1109/ROBOT.2007.363661. |
[3] |
E. Cristiani, P. Frasca and B. Piccoli, Effects of anisotropic interactions on the structure of animal groups, J. Math. Biol., 62 (2011), 569-588.
doi: 10.1007/s00285-010-0347-7. |
[4] |
F. Cucker and J.-G. Dong, A general collision-avoiding flocking framework, IEEE Trans. Autom. Control, 56 (2011), 1124-1129.
doi: 10.1109/TAC.2011.2107113. |
[5] |
F. Cucker and C. Huepe, Flocking with informed agents, Mathematics in Action, 1 (2008), 1-25.
doi: 10.5802/msia.1. |
[6] |
F. Cucker and E. Mordecki, Flocking in noisy environments, J. Math. Pures Appl., 89 (2008), 278-296.
doi: 10.1016/j.matpur.2007.12.002. |
[7] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Autom. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[8] |
F. Dalmao and E. Mordecki, Cucker-Smale flocking under hierarchical leadership and random interactions, SIAM. J. App. Math., 71 (2011), 1307-1316.
doi: 10.1137/100785910. |
[9] |
V. Gazi and K. M. Passino, Stability analysis of swarms, IEEE Trans. Autom. Control, 48 (2003), 692-697.
doi: 10.1109/TAC.2003.809765. |
[10] |
V. Gazi and K. M. Passino, Stability analysis of social foraging swarms, IEEE Trans. Syst., Man, Cybern. B, 34 (2004), 539-557.
doi: 10.1109/TSMCB.2003.817077. |
[11] |
V. Gazi and K. M. Passino, A class of attractions/repulsion functions for stable swarm aggregations, Int. J. Control, 77 (2004), 1567-1579.
doi: 10.1080/00207170412331330021. |
[12] |
S.-Y. Ha, T.-Y. Ha and J.-G. Kim, Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings, IEEE Trans. Autom. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[13] |
S.-Y. Ha, K. Lee and D. Levy, Emergence of time-asymptotic flocking in a stochastic Cucker-Smale system, Commun. Math. Sci., 7 (2009), 453-469. |
[14] |
S.-Y. Ha and E. Tadmor, From particle to kinetic and hydrodynamic descriptions of flocking, Kinetic and Related Models, 1 (2008), 415-435.
doi: 10.3934/krm.2008.1.415. |
[15] |
M. Hirsch and S. Smale, "Differential Equations, Dynamical Systems, and Linear Algebra," 60 of Pure and Applied Mathematics. Academic Press, 1974. |
[16] |
A. Jadbabaie, J. Lin and A. S. Morse, Coordination of groups of mobile autonomous agents using nearest neighbor rules, IEEE Trans. on Autom. Control, 48 (2003), 988-1001.
doi: 10.1109/TAC.2003.812781. |
[17] |
J. Kang, S.Y. Ha, E. Jeong and K. K. Kang, How do cultural classes emerge from assimilation and distinction? An extension of the Cucker-Smale flocking model, To Appear in J. Mathematical Sociology. |
[18] |
H. K. Khalil, "Nonlinear Systems," 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 2002. |
[19] |
N. Leonard and E. Fiorelli, Virtual leaders, artificial potentials and coordinated control of groups, Proc. 40th IEEE Conf. Decision Contr., (2001), 2968-2973. |
[20] |
W. Li, Stability analysis of swarms with general topology, IEEE Trans. Syst., Man, Cybern. B, 38 (2008), 1084-1097. |
[21] |
L. Perea, P. Elosegui and G. Gómez, Extension of the Cucker-Smale control law to space flight formations, Journal of Guidance, Control, and Dynamics, 32 (2009), 526-536.
doi: 10.2514/1.36269. |
[22] |
J. Shen, Cucker-Smale flocking under hierarchical leadership, SIAM J. Appl. Math, 68 (2007), 694-719.
doi: 10.1137/060673254. |
[23] |
J. J. E. Slotine and W. Li, "Applied Nonlinear Control," Englewood Cliffs, NJ: Prentice-Hall, 1991. |
[24] |
T. Vicsek and A. Zafeiris, Collective motion, Physics Reports, 517 (2012), 71-140.
doi: 10.1016/j.physrep.2012.03.004. |
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