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The DuBois-Reymond differential inclusion for autonomous optimal control problems with pointwise-constrained derivatives
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Semiconcavity of the value function for a class of differential inclusions
| 1. | Dipartimento di Matematica, Via della Ricerca Scientifica 1, Università di Roma 'Tor Vergata’, 00133 Roma, Italy |
| 2. | Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803-4918, United States |
References:
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J.-P. Aubin and H. Frankowska, "Set-Valued Analysis," Birkhäuser, Boston, 1990. |
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P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim., 29 (1991), 1322-1347.
doi: doi:10.1137/0329068. |
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P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control," Birkhäuser, Boston, 2004. |
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F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, New York, 1983. |
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F. H. Clarke, "Necessary Conditions in Dynamic Optimization," Memoir of the American Mathematical Society, 816, 2005. |
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F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, "Nonsmooth Analysis and Control Theory," Springer, New York, 1998. |
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A. Ornelas, Parametrization of Carathéodory multifunctions, Rend. Sem. Mat. Univ. Padova, 83 (1990), 33-44. |
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C. Knuckles and P. R. Wolenski, $C^1$ selections of multifunctions in one dimension, Real Analysis Exchange, 22 (1997), 655-676. |
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A. Pliś, Accessible sets in control theory, in "International Conference on Differential Equations" (Los Angeles, 1974), Academic Press, (1975), 646-650. |
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R. T. Rockafellar and R. Wets, "Variational Analysis," Springer-Verlag, Berlin Heidelberg, 1998.
doi: doi:10.1007/978-3-642-02431-3. |
show all references
References:
| [1] |
J.-P. Aubin and H. Frankowska, "Set-Valued Analysis," Birkhäuser, Boston, 1990. |
| [2] |
P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim., 29 (1991), 1322-1347.
doi: doi:10.1137/0329068. |
| [3] |
P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control," Birkhäuser, Boston, 2004. |
| [4] |
F. H. Clarke, "Optimization and Nonsmooth Analysis," Wiley, New York, 1983. |
| [5] |
F. H. Clarke, "Necessary Conditions in Dynamic Optimization," Memoir of the American Mathematical Society, 816, 2005. |
| [6] |
F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, "Nonsmooth Analysis and Control Theory," Springer, New York, 1998. |
| [7] |
A. Ornelas, Parametrization of Carathéodory multifunctions, Rend. Sem. Mat. Univ. Padova, 83 (1990), 33-44. |
| [8] |
C. Knuckles and P. R. Wolenski, $C^1$ selections of multifunctions in one dimension, Real Analysis Exchange, 22 (1997), 655-676. |
| [9] |
A. Pliś, Accessible sets in control theory, in "International Conference on Differential Equations" (Los Angeles, 1974), Academic Press, (1975), 646-650. |
| [10] |
R. T. Rockafellar and R. Wets, "Variational Analysis," Springer-Verlag, Berlin Heidelberg, 1998.
doi: doi:10.1007/978-3-642-02431-3. |
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