@article{AIHPC_2008__25_4_773_0,
author = {Cannarsa, Piermarco 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},
volume = {25},
year = {2008},
pages = {773-802},
doi = {10.1016/j.anihpc.2007.07.005},
mrnumber = {2436793},
zbl = {1145.49022},
language = {en},
url = {http://dml.mathdoc.fr/item/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, Tome 25 (2008) pp. 773-802. doi : 10.1016/j.anihpc.2007.07.005. http://gdmltest.u-ga.fr/item/AIHPC_2008__25_4_773_0/
[1] , Compactness for sub-Riemannian length-minimizers and subanalyticity, Rend. Sem. Mat. Univ. Politec. Torino 56 (4) (2001) 1-12. | MR 1845741 | Zbl 1039.53038
[2] , , , On the singularities of convex functions, Manuscripta Math. 76 (3-4) (1992) 421-435. | MR 1185029 | Zbl 0784.49011
[3] , The tangent space in sub-Riemannian geometry, in: Sub-Riemannian Geometry, Birkhäuser, 1996, pp. 1-78. | MR 1421822 | Zbl 0862.53031
[4] , , Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim. 29 (6) (1991) 1322-1347. | MR 1132185 | Zbl 0744.49011
[5] , , , Semiconcavity for optimal control problems with exit time, Discrete Contin. Dynam. Systems 6 (4) (2000) 975-997. | MR 1788264 | Zbl 1009.49024
[6] , , On a class of nonlinear time optimal control problems, Discrete Contin. Dynam. Systems 1 (2) (1995) 285-300. | MR 1355877 | Zbl 0867.49016
[7] , , Convexity properties of the minimum time function, Calc. Var. Partial Differential Equations 3 (3) (1995) 273-298. | MR 1385289 | Zbl 0836.49013
[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 2041617 | Zbl 1095.49003
[9] , Über Systeme von linearen partiellen Differentialgleichungen ester Ordnung, Math. Ann. 117 (1939) 98-105. | JFM 65.0398.01 | MR 1880
[10] , Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons Inc., New York, 1983. | MR 709590 | Zbl 0582.49001
[11] , Necessary conditions in dynamic optimization, Mem. Amer. Math. Soc. 173 (816) (2005). | MR 2117692 | Zbl 1093.49017
[12] , , , , Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, vol. 178, Springer-Verlag, New York, 1998. | MR 1488695 | Zbl 1047.49500
[13] , Horizontal path spaces and Carnot-Carathéodory metrics, Pacific J. Math. 161 (2) (1993) 255-286. | MR 1242199 | Zbl 0797.49033
[14] I. Kupka, Géométrie sous-riemannienne, Astérisque, (241):Exp. No. 817, 5, 351-380, 1997. Séminaire Bourbaki, vol. 1995/96. | Numdam | MR 1472545 | Zbl 0893.53013
[15] , A Tour of Subriemannian Geometries, their Geodesics and Applications, Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002. | MR 1867362 | Zbl 1044.53022
[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 247552 | Zbl 0154.37004
[18] , Existence of Lipschitz and semiconcave control-Lyapunov functions, SIAM J. Control Optim. 39 (4) (2000) 1043-1064. | MR 1814266 | Zbl 0982.93068
[19] , Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim. 41 (3) (2002) 659-681. | MR 1939865 | Zbl 1034.93053
[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 2079683 | Zbl pre02222962
[21] , A Morse-Sard theorem for the distance function on Riemannian manifolds, Manuscripta Math. 113 (2004) 251-265. | MR 2128549 | Zbl 1051.53050
[22] , À propos des sphères sous-riemanniennes, Bull. Belg. Math. Soc. Simon Stevin 13 (3) (2006) 521-526. | MR 2307687 | Zbl 1135.53021
[23] L. Rifford, E. Trélat, On the stabilization problem for nonholonomic distributions, J. Eur. Math. Soc., in press. | Zbl pre05545778
[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 1778212 | Zbl 0964.49021
[25] , Fat bundles and symplectic manifolds, Adv. in Math. 37 (1980) 239-250. | MR 591728 | Zbl 0449.53035