@article{AIHPC_2008__25_4_773_0, author = {Cannarsa, P. and Rifford, L.}, title = {Semiconcavity results for optimal control problems admitting no singular minimizing controls}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {773--802}, publisher = {Elsevier}, volume = {25}, number = {4}, year = {2008}, doi = {10.1016/j.anihpc.2007.07.005}, mrnumber = {2436793}, zbl = {1145.49022}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2007.07.005/} }
TY - JOUR AU - Cannarsa, P. AU - Rifford, L. TI - Semiconcavity results for optimal control problems admitting no singular minimizing controls JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 773 EP - 802 VL - 25 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2007.07.005/ DO - 10.1016/j.anihpc.2007.07.005 LA - en ID - AIHPC_2008__25_4_773_0 ER -
%0 Journal Article %A Cannarsa, P. %A Rifford, L. %T Semiconcavity results for optimal control problems admitting no singular minimizing controls %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 773-802 %V 25 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2007.07.005/ %R 10.1016/j.anihpc.2007.07.005 %G en %F AIHPC_2008__25_4_773_0
Cannarsa, P.; Rifford, L. Semiconcavity results for optimal control problems admitting no singular minimizing controls. Annales de l'I.H.P. Analyse non linéaire, Volume 25 (2008) no. 4, pp. 773-802. doi : 10.1016/j.anihpc.2007.07.005. http://www.numdam.org/articles/10.1016/j.anihpc.2007.07.005/
[1] Compactness for sub-Riemannian length-minimizers and subanalyticity, Rend. Sem. Mat. Univ. Politec. Torino 56 (4) (2001) 1-12. | MR | Zbl
,[2] On the singularities of convex functions, Manuscripta Math. 76 (3-4) (1992) 421-435. | MR | Zbl
, , ,[3] The tangent space in sub-Riemannian geometry, in: Sub-Riemannian Geometry, Birkhäuser, 1996, pp. 1-78. | MR | Zbl
,[4] Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim. 29 (6) (1991) 1322-1347. | MR | Zbl
, ,[5] Semiconcavity for optimal control problems with exit time, Discrete Contin. Dynam. Systems 6 (4) (2000) 975-997. | MR | Zbl
, , ,[6] On a class of nonlinear time optimal control problems, Discrete Contin. Dynam. Systems 1 (2) (1995) 285-300. | MR | Zbl
, ,[7] Convexity properties of the minimum time function, Calc. Var. Partial Differential Equations 3 (3) (1995) 273-298. | MR | Zbl
, ,[8] Semiconcave Functions, Hamilton-Jacobi Equations, and Optimal Control, Progress in Nonlinear Differential Equations and their Applications, vol. 58, Birkhäuser Boston Inc., Boston, MA, 2004. | MR | Zbl
, ,[9] Über Systeme von linearen partiellen Differentialgleichungen ester Ordnung, Math. Ann. 117 (1939) 98-105. | JFM | MR
,[10] Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons Inc., New York, 1983. | MR | Zbl
,[11] Necessary conditions in dynamic optimization, Mem. Amer. Math. Soc. 173 (816) (2005). | MR | Zbl
,[12] Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, vol. 178, Springer-Verlag, New York, 1998. | MR | Zbl
, , , ,[13] Horizontal path spaces and Carnot-Carathéodory metrics, Pacific J. Math. 161 (2) (1993) 255-286. | MR | Zbl
,[14] I. Kupka, Géométrie sous-riemannienne, Astérisque, (241):Exp. No. 817, 5, 351-380, 1997. Séminaire Bourbaki, vol. 1995/96. | Numdam | MR | Zbl
[15] A Tour of Subriemannian Geometries, their Geodesics and Applications, Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002. | MR | Zbl
,[16] About connecting two points of a completely nonholonomic space by admissible curve, Uch. Zapiski Ped. Inst. Libknechta 2 (1938) 83-94.
,[17] The exponential map for the Lagrange problem on differentiable manifold, Philos. Trans. Roy. Soc. London Ser. A, Math. and Phys. 1127 (1967) 299-344. | MR | Zbl
,[18] Existence of Lipschitz and semiconcave control-Lyapunov functions, SIAM J. Control Optim. 39 (4) (2000) 1043-1064. | MR | Zbl
,[19] Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim. 41 (3) (2002) 659-681. | MR | Zbl
,[20] The stabilization problem: AGAS and SRS feedbacks, in: Optimal Control, Stabilization, and Nonsmooth Analysis, Lectures Notes in Control and Information Sciences, vol. 301, Springer-Verlag, Heidelberg, 2004, pp. 173-184. | MR
,[21] A Morse-Sard theorem for the distance function on Riemannian manifolds, Manuscripta Math. 113 (2004) 251-265. | MR | Zbl
,[22] À propos des sphères sous-riemanniennes, Bull. Belg. Math. Soc. Simon Stevin 13 (3) (2006) 521-526. | MR | Zbl
,[23] L. Rifford, E. Trélat, On the stabilization problem for nonholonomic distributions, J. Eur. Math. Soc., in press.
[24] Some properties of the value function and its level sets for affine control systems with quadratic cost, J. Dynamical Control Systems 6 (4) (2000) 511-541. | MR | Zbl
,[25] Fat bundles and symplectic manifolds, Adv. in Math. 37 (1980) 239-250. | MR | Zbl
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