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Regular discretizations in optimal control theory
1. | Department of Applied Mathematics, University of Salamanca, Salamanca 37008 |
2. | IUFFyM-USAL and Real Academia de Ciencias, Plaza de la Merced 1-4, 37008 Salamanca |
References:
[1] |
M. Aldeen and F. Crusca, Quadratic cost function design for linear optimal control systems,, in TENCON '92., (1992), 958.
doi: 10.1109/TENCON.1992.271828. |
[2] |
V. I. Arnol'd, V. V. Kozlov and A. I. Neĭshtadt, Dynamical Systems. III,, Encyclopaedia of Mathematical Sciences, (1988).
doi: 10.1007/978-3-642-61551-1. |
[3] |
R. Benito and D. Martín de Diego, Discrete vakonomic mechanics,, J. Math. Phys., 46 (2005).
doi: 10.1063/1.2008214. |
[4] |
A. M. Bloch, Nonholonomic Mechanics and Control,, Interdisciplinary Applied Mathematics, (2003).
doi: 10.1007/b97376. |
[5] |
A. Fernández, P. L García and Ana G Sípols, Variational integrators in discrete time-dependent optimal control theory,, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 106 (2012), 173.
doi: 10.1007/s13398-011-0037-3. |
[6] |
P. L. García, A. García and C. Rodrigo, Cartan forms for first order constrained variational problems,, J. Geom. Phys., 56 (2006), 571.
doi: 10.1016/j.geomphys.2005.04.002. |
[7] |
P. L. García, A. Fernández and C. Rodrigo, Variational integrators for discrete Lagrange problems,, J. Geom. Mech., 2 (2010), 343.
doi: 10.3934/jgm.2010.2.343. |
[8] |
V. Guibout and A. Bloch, A discrete maximum principle for solving optimal control problems,, in CDC. 43rd IEEE Conference on Decision and Control, (2004), 1806.
doi: 10.1109/CDC.2004.1430309. |
[9] |
F. Jiménez and D. Martín de Diego, A geometric approach to discrete mechanics for optimal control theory,, in Proceedings of the IEEE Conference on Decision and Control, (2010), 5426. Google Scholar |
[10] |
F. Jiménez, M. Kobilarov and Martín de Diego, Discrete variational optimal control,, accepted in Journal of Nonlinear Science, (2012). Google Scholar |
[11] |
M. Kobilarov and J. E. Marsden, Discrete geometric optimal control on Lie groups,, IEEE Transactions on Robotics, 27 (2011), 641.
doi: 10.1109/TRO.2011.2139130. |
[12] |
T. Lee, N. McClamroch and M. Leok, Optimal control of a rigid body using geometrically exact computations on SE(3),, in Proceedings of the IEEE Conference on Decision and Control, (2006), 2710.
doi: 10.1109/CDC.2006.376687. |
[13] |
M. de León, D. Martín de Diego and A. Santamaría-Merino, Discrete variational integrators and optimal control theory,, Adv. Comput. Math., 26 (2006), 251.
doi: 10.1007/s10444-004-4093-5. |
[14] |
M. de León, J. C. Marrero and D. Martín de Diego, Vakonomic mechanics versus non-holonomic mechanics: A unified geometrical approach,, J. Geom. Phys., 35 (2000), 126.
doi: 10.1016/S0393-0440(00)00004-8. |
[15] |
M. Leok, Foundations of Computational Geometric Mechanics,, Ph.D. Thesis, (2004).
|
[16] |
J. E. Marsden, G. W. Patrick and S. Shkoller, Multisymplectic geometry, variational integrators, and nonlinear PDEs,, Comm. in Math. Phys., 199 (1998), 351.
doi: 10.1007/s002200050505. |
[17] |
J. E. Marsden and M. West, Discrete mechanics and variational integrators,, Acta Numerica, 10 (2001), 317.
doi: 10.1017/S096249290100006X. |
[18] |
J. Moser and A. P. Veselov, Discrete versions of some classical integrable systems and factorization of matrix polynomials,, Comm. Math. Phys., 139 (1991), 217.
doi: 10.1007/BF02352494. |
[19] |
S. Ober-Blöbaum, O. Junge and J. E. Marsden, Discrete mechanics and optimal control: An analysis,, ESAIM Control Optim. Calc. Var., 17 (2011), 322.
doi: 10.1051/cocv/2010012. |
[20] |
P. Piccione and D. V. Tausk, Lagrangian and Hamiltonian formalism for constrained variational problems,, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), 1417.
|
[21] |
M. West, Variational Integrators,, Ph.D. Thesis, (2004).
|
show all references
References:
[1] |
M. Aldeen and F. Crusca, Quadratic cost function design for linear optimal control systems,, in TENCON '92., (1992), 958.
doi: 10.1109/TENCON.1992.271828. |
[2] |
V. I. Arnol'd, V. V. Kozlov and A. I. Neĭshtadt, Dynamical Systems. III,, Encyclopaedia of Mathematical Sciences, (1988).
doi: 10.1007/978-3-642-61551-1. |
[3] |
R. Benito and D. Martín de Diego, Discrete vakonomic mechanics,, J. Math. Phys., 46 (2005).
doi: 10.1063/1.2008214. |
[4] |
A. M. Bloch, Nonholonomic Mechanics and Control,, Interdisciplinary Applied Mathematics, (2003).
doi: 10.1007/b97376. |
[5] |
A. Fernández, P. L García and Ana G Sípols, Variational integrators in discrete time-dependent optimal control theory,, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 106 (2012), 173.
doi: 10.1007/s13398-011-0037-3. |
[6] |
P. L. García, A. García and C. Rodrigo, Cartan forms for first order constrained variational problems,, J. Geom. Phys., 56 (2006), 571.
doi: 10.1016/j.geomphys.2005.04.002. |
[7] |
P. L. García, A. Fernández and C. Rodrigo, Variational integrators for discrete Lagrange problems,, J. Geom. Mech., 2 (2010), 343.
doi: 10.3934/jgm.2010.2.343. |
[8] |
V. Guibout and A. Bloch, A discrete maximum principle for solving optimal control problems,, in CDC. 43rd IEEE Conference on Decision and Control, (2004), 1806.
doi: 10.1109/CDC.2004.1430309. |
[9] |
F. Jiménez and D. Martín de Diego, A geometric approach to discrete mechanics for optimal control theory,, in Proceedings of the IEEE Conference on Decision and Control, (2010), 5426. Google Scholar |
[10] |
F. Jiménez, M. Kobilarov and Martín de Diego, Discrete variational optimal control,, accepted in Journal of Nonlinear Science, (2012). Google Scholar |
[11] |
M. Kobilarov and J. E. Marsden, Discrete geometric optimal control on Lie groups,, IEEE Transactions on Robotics, 27 (2011), 641.
doi: 10.1109/TRO.2011.2139130. |
[12] |
T. Lee, N. McClamroch and M. Leok, Optimal control of a rigid body using geometrically exact computations on SE(3),, in Proceedings of the IEEE Conference on Decision and Control, (2006), 2710.
doi: 10.1109/CDC.2006.376687. |
[13] |
M. de León, D. Martín de Diego and A. Santamaría-Merino, Discrete variational integrators and optimal control theory,, Adv. Comput. Math., 26 (2006), 251.
doi: 10.1007/s10444-004-4093-5. |
[14] |
M. de León, J. C. Marrero and D. Martín de Diego, Vakonomic mechanics versus non-holonomic mechanics: A unified geometrical approach,, J. Geom. Phys., 35 (2000), 126.
doi: 10.1016/S0393-0440(00)00004-8. |
[15] |
M. Leok, Foundations of Computational Geometric Mechanics,, Ph.D. Thesis, (2004).
|
[16] |
J. E. Marsden, G. W. Patrick and S. Shkoller, Multisymplectic geometry, variational integrators, and nonlinear PDEs,, Comm. in Math. Phys., 199 (1998), 351.
doi: 10.1007/s002200050505. |
[17] |
J. E. Marsden and M. West, Discrete mechanics and variational integrators,, Acta Numerica, 10 (2001), 317.
doi: 10.1017/S096249290100006X. |
[18] |
J. Moser and A. P. Veselov, Discrete versions of some classical integrable systems and factorization of matrix polynomials,, Comm. Math. Phys., 139 (1991), 217.
doi: 10.1007/BF02352494. |
[19] |
S. Ober-Blöbaum, O. Junge and J. E. Marsden, Discrete mechanics and optimal control: An analysis,, ESAIM Control Optim. Calc. Var., 17 (2011), 322.
doi: 10.1051/cocv/2010012. |
[20] |
P. Piccione and D. V. Tausk, Lagrangian and Hamiltonian formalism for constrained variational problems,, Proc. Roy. Soc. Edinburgh Sect. A, 132 (2002), 1417.
|
[21] |
M. West, Variational Integrators,, Ph.D. Thesis, (2004).
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