Semiconcavity of the value function for a class of differential inclusions

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April 2011, 29(2): 453-466. doi: 10.3934/dcds.2011.29.453

Semiconcavity of the value function for a class of differential inclusions

Piermarco Cannarsa ^1, and Peter R. Wolenski ^2,

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

Received September 2009 Revised March 2010 Published October 2010

Abstract
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We provide intrinsic sufficient conditions on a multifunction $F$ and endpoint data φ so that the value function associated to the Mayer problem is semiconcave.

Keywords: differential inclusions, Semiconcave functions, optimal control, Mayer problems..

Mathematics Subject Classification: Primary: 34A60, 49J53; Secondary: 49J1.

Citation: Piermarco Cannarsa, Peter R. Wolenski. Semiconcavity of the value function for a class of differential inclusions. Discrete & Continuous Dynamical Systems - A, 2011, 29 (2) : 453-466. doi: 10.3934/dcds.2011.29.453

References:

[1]	J.-P. Aubin and H. Frankowska, "Set-Valued Analysis,", Birkhäuser, (1990).
[2]	P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in control theory,, SIAM J. Control Optim., 29 (1991), 1322. doi: doi:10.1137/0329068.
[3]	P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control,", Birkhäuser, (2004).
[4]	F. H. Clarke, "Optimization and Nonsmooth Analysis,", Wiley, (1983).
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[6]	F. H. Clarke, Yu. S. Ledyaev, R. J. Stern, and P. R. Wolenski, "Nonsmooth Analysis and Control Theory,", Springer, (1998).
[7]	A. Ornelas, Parametrization of Carathéodory multifunctions,, Rend. Sem. Mat. Univ. Padova, 83 (1990), 33.
[8]	C. Knuckles and P. R. Wolenski, $C^1$ selections of multifunctions in one dimension,, Real Analysis Exchange, 22 (1997), 655.
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[10]	R. T. Rockafellar and R. Wets, "Variational Analysis,", Springer-Verlag, (1998). doi: doi:10.1007/978-3-642-02431-3.

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References:

[1]	J.-P. Aubin and H. Frankowska, "Set-Valued Analysis,", Birkhäuser, (1990).
[2]	P. Cannarsa and H. Frankowska, Some characterizations of optimal trajectories in control theory,, SIAM J. Control Optim., 29 (1991), 1322. doi: doi:10.1137/0329068.
[3]	P. Cannarsa and C. Sinestrari, "Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control,", Birkhäuser, (2004).
[4]	F. H. Clarke, "Optimization and Nonsmooth Analysis,", Wiley, (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, (1998).
[7]	A. Ornelas, Parametrization of Carathéodory multifunctions,, Rend. Sem. Mat. Univ. Padova, 83 (1990), 33.
[8]	C. Knuckles and P. R. Wolenski, $C^1$ selections of multifunctions in one dimension,, Real Analysis Exchange, 22 (1997), 655.
[9]	A. Pliś, Accessible sets in control theory,, in, (1975), 646.
[10]	R. T. Rockafellar and R. Wets, "Variational Analysis,", Springer-Verlag, (1998). doi: doi:10.1007/978-3-642-02431-3.

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