On the subanalyticity of Carnot-Caratheodory distances
Agrachev, Andrei ; Gauthier, Jean-Paul
Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001), p. 359-382 / Harvested from Numdam
Publié le : 2001-01-01
@article{AIHPC_2001__18_3_359_0,
     author = {Agrachev, Andrei A. and Gauthier, Jean-Paul},
     title = {On the subanalyticity of Carnot-Caratheodory distances},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {18},
     year = {2001},
     pages = {359-382},
     zbl = {1001.93014},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2001__18_3_359_0}
}
Agrachev, Andrei; Gauthier, Jean-Paul. On the subanalyticity of Carnot-Caratheodory distances. Annales de l'I.H.P. Analyse non linéaire, Tome 18 (2001) pp. 359-382. http://gdmltest.u-ga.fr/item/AIHPC_2001__18_3_359_0/

[1] Agrachev A.A, Compactness for sub-Riemannian length-minimizers and subanalyticity, Rend. Semin. Mat. Torino 56 (1998). | MR 1845741 | Zbl 1039.53038

[2] Agrachev A.A, Gamkrelidze R.V, Sarychev A.V, Local invariants of smooth control systems, Acta Appl. Math. 14 (1989) 191-237. | MR 995286 | Zbl 0681.49018

[3] Agrachev A.A, Sarychev A.V, Filtrations of a Lie algebra of vector fields and nilpotent approximation of control systems, Dokl. Akad. Nauk SSSR 295 (1987) 777-781, English transl. in Soviet Math. Dokl. 36 (1988) 104-108. | Zbl 0850.93106

[4] Agrachev A.A, Sarychev A.V, Abnormal sub-Riemannian geodesics: Morse index and rigidity, Annales de l'Institut Henri Poincaré, Analyse non linéaire 13 (1996) 635-690. | Numdam | MR 1420493 | Zbl 0866.58023

[5] Agrachev A.A, Sarychev A.V, Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity, J. ESAIM: Control, Optimisation and Calculus of Variations 4 (1999) 377-403. | Numdam | MR 1693912 | Zbl 0978.53065

[6] Agrachev A.A, Bonnard B, Chyba M, Kupka I, Sub-Riemannian sphere in Martinet flat case, J. ESAIM: Control, Optimisation and Calculus of Variations 2 (1997) 377-448. | Numdam | MR 1483765 | Zbl 0902.53033

[7] Bellaïche A, The tangent space in sub-Riemannian geometry, in: Sub-Riemannian Geometry, Birkhäuser, 1996, pp. 1-78. | MR 1421822 | Zbl 0862.53031

[8] Bianchini R.M, Stefani G, Graded approximations and controllability along a trajectory, SIAM J. Control Optim. 28 (1990) 903-924. | MR 1051629 | Zbl 0712.93005

[9] Bonnard B., Chyba M., Méthodes géométriques et analytique pour étudier l'application exponentiele, la sphère et le front d'onde en géometrie SR dans le cas Martinet, J. ESAIM: Control, Optimisation and Calculus of Variations, submitted. | Numdam | Zbl 0929.53016

[10] Bonnard B., Launay G., Trélat E., The transcendence we need to compute the sphere and the wave front in Martinet SR-geometry, in: Proc. Int. Confer. Dedicated to Pontryagin, Moscow, September 1998, to appear. | MR 1871126 | Zbl 0988.35008

[11] Chow W.-L, Über Systeme von linearen partiellen Differentialgleichungen ester Ordnung, Math. Ann. 117 (1939) 98-105. | JFM 65.0398.01 | MR 1880

[12] Filippov A.F, On certain questions in the theory of optimal control, Vestnik Moskov. Univ., Ser. Matem., Mekhan., Astron. 2 (1959) 25-32. | Zbl 0090.06902

[13] Gabrielov A, Projections of semi analytic sets, Funct. Anal. Appl. 2 (1968) 282-291. | Zbl 0179.08503

[14] Gauthier J.-P, Kupka I, Observability for systems with more outputs than inputs and asymptotic observers, Mathem. Zeitschrift 223 (1996) 47-78. | MR 1408862 | Zbl 0863.93008

[15] Ge Zhong, Horizontal path space and Carnot-Caratheodory metric, Pacific J. Math. 161 (1993) 255-286. | Zbl 0797.49033

[16] Hironaka H, Subanalytic sets, in: Numbers Theory, Algebraic Geometry, and Commutative Algebra (in honor of V. Akizuki), Tokyo, 1973, pp. 453-493. | MR 377101 | Zbl 0297.32008

[17] Jacquet S, Subanalyticity of the sub-Riemannian distance, J. Dynamical and Control Systems 5 (1999). | MR 1706801 | Zbl 0963.53014

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

[19] Stefani G, On local controllability of a scalar-input system, in: Byrnes , Lindquist (Eds.), Theory and Appl. of Nonlinear Control Syst., North Holland, Amsterdam, 1986, pp. 167-179. | MR 935375 | Zbl 0603.93006

[20] Sussmann H.J, Optimal control and piecewise analyticity of the distance function, in: Ioffe A, Reich S (Eds.), Pitman Research Notes in Mathematics, Longman Publishers, 1992, pp. 298-310. | MR 1184651 | Zbl 0772.49019

[21] Sussmann H.J, Trajectory regularity and real analyticity, in: Proc. 25th CDC Conference, Athens, Greece, 1986, pp. 592-595.

[22] Sussmann H.J, A weak regularity theorem for real-analytic optimal control problems, Revista Mathematica Iberoamericana 2 (3) (1986) 307-317. | MR 908055 | Zbl 0638.49018

[23] Tamm M, Subanalytic sets in the calculus of variations, Acta Mathematica 46 (1981) 167-199. | MR 611382 | Zbl 0478.58010