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Sparse control of alignment models in high dimension
1. | Technische Universität München, Fakultät Mathematik, Boltzmannstraße 3, D-85748 Garching |
2. | Technische Universität München, Fakultät Mathematik, Boltzmannstrasse 3, D-85748 Garching, Germany, Germany |
References:
[1] |
S. Ahn, H.-O. Bae, S.-Y. Ha, Y. Kim and H. Lim, Application of flocking mechanism to the modeling of stochastic volatility, Math. Models Methods Appl. Sci., 23 (2013), 1603-1628.
doi: 10.1142/S0218202513500176. |
[2] |
R. G. Baraniuk and M. B. Wakin, Random projections of smooth manifolds, Found. Comput. Math., 9 (2009), 51-77.
doi: 10.1007/s10208-007-9011-z. |
[3] |
M. Bongini and M. Fornasier, Sparse stabilization of dynamical systems driven by attraction and avoidance forces, Netw. Heterog. Media, 9 (2014), 1-31.
doi: 10.3934/nhm.2014.9.1. |
[4] |
M. Bongini, D. Kalise and M. Fornasier, (Un)conditional consensus emergence under perturbed and decentralized feedback controls, Discrete Contin. Dynam. Systems, 35 (2015), 4071-4094.
doi: 10.3934/dcds.2015.35.4071. |
[5] |
J. Bouvrie and M. Maggioni, Geometric multiscale reduction for autonomous and controlled nonlinear systems, in 51st IEEE Conference on Decision and Control (CDC), 2012, 4320-4327.
doi: 10.1109/CDC.2012.6425873. |
[6] |
M. Caponigro, M. Fornasier, B. Piccoli and E. Trelat, Sparse stabilization and control of the Cucker-Smale model, Math. Control Relat. Fields, 3 (2013), 447-466.
doi: 10.3934/mcrf.2013.3.447. |
[7] |
M. Caponigro, M. Fornasier, B. Piccoli and E. Trelat, Sparse stabilization and control of alignment models, Math. Models Methods Appl. Sci., 25 (2015), 521-564.
doi: 10.1142/S0218202515400059. |
[8] |
F. H. Clarke, Y. S. Ledyaev, E. D. Sontag and A. I. Subbotin, Asymptotic controllability implies feedback stabilization, IEEE Trans. Automat. Control, 42 (1997), 1394-1407.
doi: 10.1109/9.633828. |
[9] |
R. R. Coifman and M. J. Hirn, Diffusion maps for changing data, Appl. Comput. Harmon. Anal., 36 (2014), 79-107.
doi: 10.1016/j.acha.2013.03.001. |
[10] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[11] |
F. Cucker and S. Smale, On the mathematics of emergence, Jpn. J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[12] |
S. Dasgupta and A. Gupta, An elementary proof of a theorem of Johnson and Lindenstrauss, Random Structures Algorithms, 22 (2003), 60-65.
doi: 10.1002/rsa.10073. |
[13] |
S. Dirksen, Dimensionality reduction with subgaussian matrices: A unified theory, arXiv:1402.3973, 2014. |
[14] |
M. Fornasier, J. Haškovec and J. Vybíral, Particle systems and kinetic equations modeling interacting agents in high dimension, Multiscale Model. Simul., 9 (2011), 1727-1764.
doi: 10.1137/110830617. |
[15] |
M. Fornasier, B. Piccoli and F. Rossi, Mean-field sparse optimal control, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 372 (2014), 20130400, 21PP.
doi: 10.1098/rsta.2013.0400. |
[16] |
M. Fornasier and F. Solombrino, Mean-field optimal control, ESAIM Control Optim. Calc. Var., 20 (2014), 1123-1152.
doi: 10.1051/cocv/2014009. |
[17] |
S.-Y. Ha, T. H. Ha and J.-H. Kim, Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings, IEEE Trans. Automat. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[18] |
W. B. Johnson and J. Lindenstrauss, Extensions of Lipschitz mappings into a Hilbert space, in Conference in modern analysis and probability, New Haven, Conn., 1982, Contemp. Math., 26, Amer. Math. Soc., Providence, RI, 1984, 189-206.
doi: 10.1090/conm/026/737400. |
show all references
References:
[1] |
S. Ahn, H.-O. Bae, S.-Y. Ha, Y. Kim and H. Lim, Application of flocking mechanism to the modeling of stochastic volatility, Math. Models Methods Appl. Sci., 23 (2013), 1603-1628.
doi: 10.1142/S0218202513500176. |
[2] |
R. G. Baraniuk and M. B. Wakin, Random projections of smooth manifolds, Found. Comput. Math., 9 (2009), 51-77.
doi: 10.1007/s10208-007-9011-z. |
[3] |
M. Bongini and M. Fornasier, Sparse stabilization of dynamical systems driven by attraction and avoidance forces, Netw. Heterog. Media, 9 (2014), 1-31.
doi: 10.3934/nhm.2014.9.1. |
[4] |
M. Bongini, D. Kalise and M. Fornasier, (Un)conditional consensus emergence under perturbed and decentralized feedback controls, Discrete Contin. Dynam. Systems, 35 (2015), 4071-4094.
doi: 10.3934/dcds.2015.35.4071. |
[5] |
J. Bouvrie and M. Maggioni, Geometric multiscale reduction for autonomous and controlled nonlinear systems, in 51st IEEE Conference on Decision and Control (CDC), 2012, 4320-4327.
doi: 10.1109/CDC.2012.6425873. |
[6] |
M. Caponigro, M. Fornasier, B. Piccoli and E. Trelat, Sparse stabilization and control of the Cucker-Smale model, Math. Control Relat. Fields, 3 (2013), 447-466.
doi: 10.3934/mcrf.2013.3.447. |
[7] |
M. Caponigro, M. Fornasier, B. Piccoli and E. Trelat, Sparse stabilization and control of alignment models, Math. Models Methods Appl. Sci., 25 (2015), 521-564.
doi: 10.1142/S0218202515400059. |
[8] |
F. H. Clarke, Y. S. Ledyaev, E. D. Sontag and A. I. Subbotin, Asymptotic controllability implies feedback stabilization, IEEE Trans. Automat. Control, 42 (1997), 1394-1407.
doi: 10.1109/9.633828. |
[9] |
R. R. Coifman and M. J. Hirn, Diffusion maps for changing data, Appl. Comput. Harmon. Anal., 36 (2014), 79-107.
doi: 10.1016/j.acha.2013.03.001. |
[10] |
F. Cucker and S. Smale, Emergent behavior in flocks, IEEE Trans. Automat. Control, 52 (2007), 852-862.
doi: 10.1109/TAC.2007.895842. |
[11] |
F. Cucker and S. Smale, On the mathematics of emergence, Jpn. J. Math., 2 (2007), 197-227.
doi: 10.1007/s11537-007-0647-x. |
[12] |
S. Dasgupta and A. Gupta, An elementary proof of a theorem of Johnson and Lindenstrauss, Random Structures Algorithms, 22 (2003), 60-65.
doi: 10.1002/rsa.10073. |
[13] |
S. Dirksen, Dimensionality reduction with subgaussian matrices: A unified theory, arXiv:1402.3973, 2014. |
[14] |
M. Fornasier, J. Haškovec and J. Vybíral, Particle systems and kinetic equations modeling interacting agents in high dimension, Multiscale Model. Simul., 9 (2011), 1727-1764.
doi: 10.1137/110830617. |
[15] |
M. Fornasier, B. Piccoli and F. Rossi, Mean-field sparse optimal control, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., 372 (2014), 20130400, 21PP.
doi: 10.1098/rsta.2013.0400. |
[16] |
M. Fornasier and F. Solombrino, Mean-field optimal control, ESAIM Control Optim. Calc. Var., 20 (2014), 1123-1152.
doi: 10.1051/cocv/2014009. |
[17] |
S.-Y. Ha, T. H. Ha and J.-H. Kim, Emergent behavior of a Cucker-Smale type particle model with nonlinear velocity couplings, IEEE Trans. Automat. Control, 55 (2010), 1679-1683.
doi: 10.1109/TAC.2010.2046113. |
[18] |
W. B. Johnson and J. Lindenstrauss, Extensions of Lipschitz mappings into a Hilbert space, in Conference in modern analysis and probability, New Haven, Conn., 1982, Contemp. Math., 26, Amer. Math. Soc., Providence, RI, 1984, 189-206.
doi: 10.1090/conm/026/737400. |
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