Semiconcavity results for optimal control problems admitting no singular minimizing controls
Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 4, pp. 773-802.
@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, Tome 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] Agrachev A., Compactness for sub-Riemannian length-minimizers and subanalyticity, Rend. Sem. Mat. Univ. Politec. Torino 56 (4) (2001) 1-12. | MR | Zbl

[2] Alberti G., Ambrosio L., Cannarsa P., On the singularities of convex functions, Manuscripta Math. 76 (3-4) (1992) 421-435. | MR | Zbl

[3] Bellaiche A., The tangent space in sub-Riemannian geometry, in: Sub-Riemannian Geometry, Birkhäuser, 1996, pp. 1-78. | MR | Zbl

[4] Cannarsa P., Frankowska H., Some characterizations of optimal trajectories in control theory, SIAM J. Control Optim. 29 (6) (1991) 1322-1347. | MR | Zbl

[5] Cannarsa P., Pignotti C., Sinestrari C., Semiconcavity for optimal control problems with exit time, Discrete Contin. Dynam. Systems 6 (4) (2000) 975-997. | MR | Zbl

[6] Cannarsa P., Sinestrari C., On a class of nonlinear time optimal control problems, Discrete Contin. Dynam. Systems 1 (2) (1995) 285-300. | MR | Zbl

[7] Cannarsa P., Sinestrari C., Convexity properties of the minimum time function, Calc. Var. Partial Differential Equations 3 (3) (1995) 273-298. | MR | Zbl

[8] Cannarsa P., Sinestrari C., 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] Chow C.-L., Über Systeme von linearen partiellen Differentialgleichungen ester Ordnung, Math. Ann. 117 (1939) 98-105. | JFM | MR

[10] Clarke F.H., Optimization and Nonsmooth Analysis, Canadian Mathematical Society Series of Monographs and Advanced Texts, John Wiley & Sons Inc., New York, 1983. | MR | Zbl

[11] Clarke F., Necessary conditions in dynamic optimization, Mem. Amer. Math. Soc. 173 (816) (2005). | MR | Zbl

[12] Clarke F.H., Ledyaev Yu.S., Stern R.J., Wolenski P.R., Nonsmooth Analysis and Control Theory, Graduate Texts in Mathematics, vol. 178, Springer-Verlag, New York, 1998. | MR | Zbl

[13] Ge Z., 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] Montgomery R., A Tour of Subriemannian Geometries, their Geodesics and Applications, Mathematical Surveys and Monographs, vol. 91, American Mathematical Society, Providence, RI, 2002. | MR | Zbl

[16] Rashevsky P.K., About connecting two points of a completely nonholonomic space by admissible curve, Uch. Zapiski Ped. Inst. Libknechta 2 (1938) 83-94.

[17] Rayer C.B., 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] Rifford L., Existence of Lipschitz and semiconcave control-Lyapunov functions, SIAM J. Control Optim. 39 (4) (2000) 1043-1064. | MR | Zbl

[19] Rifford L., Semiconcave control-Lyapunov functions and stabilizing feedbacks, SIAM J. Control Optim. 41 (3) (2002) 659-681. | MR | Zbl

[20] Rifford L., 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] Rifford L., A Morse-Sard theorem for the distance function on Riemannian manifolds, Manuscripta Math. 113 (2004) 251-265. | MR | Zbl

[22] Rifford L., 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] Trélat E., 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] Weinstein A., Fat bundles and symplectic manifolds, Adv. in Math. 37 (1980) 239-250. | MR | Zbl

Cité par Sources :