On the subanalyticity of Carnot–Caratheodory distances
Andrei Agrachev; Jean-Paul Gauthier
Annales de l'I.H.P. Analyse non linéaire (2001)
- Volume: 18, Issue: 3, page 359-382
- ISSN: 0294-1449
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topAgrachev, Andrei, and Gauthier, Jean-Paul. "On the subanalyticity of Carnot–Caratheodory distances." Annales de l'I.H.P. Analyse non linéaire 18.3 (2001): 359-382. <http://eudml.org/doc/78524>.
@article{Agrachev2001,
author = {Agrachev, Andrei, Gauthier, Jean-Paul},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {Riemannian manifold; optimal controls; Carnot-Caratheodory distance},
language = {eng},
number = {3},
pages = {359-382},
publisher = {Elsevier},
title = {On the subanalyticity of Carnot–Caratheodory distances},
url = {http://eudml.org/doc/78524},
volume = {18},
year = {2001},
}
TY - JOUR
AU - Agrachev, Andrei
AU - Gauthier, Jean-Paul
TI - On the subanalyticity of Carnot–Caratheodory distances
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2001
PB - Elsevier
VL - 18
IS - 3
SP - 359
EP - 382
LA - eng
KW - Riemannian manifold; optimal controls; Carnot-Caratheodory distance
UR - http://eudml.org/doc/78524
ER -
References
top- [1] Agrachev A.A, Compactness for sub-Riemannian length-minimizers and subanalyticity, Rend. Semin. Mat. Torino56 (1998). Zbl1039.53038MR1845741
- [2] Agrachev A.A, Gamkrelidze R.V, Sarychev A.V, Local invariants of smooth control systems, Acta Appl. Math.14 (1989) 191-237. Zbl0681.49018MR995286
- [3] Agrachev A.A, Sarychev A.V, Filtrations of a Lie algebra of vector fields and nilpotent approximation of control systems, Dokl. Akad. Nauk SSSR295 (1987) 777-781, English transl. in Soviet Math. Dokl. 36 (1988) 104–108. Zbl0850.93106
- [4] Agrachev A.A, Sarychev A.V, Abnormal sub-Riemannian geodesics: Morse index and rigidity, Annales de l'Institut Henri Poincaré, Analyse non linéaire13 (1996) 635-690. Zbl0866.58023MR1420493
- [5] Agrachev A.A, Sarychev A.V, Sub-Riemannian metrics: minimality of abnormal geodesics versus subanalyticity, J. ESAIM: Control, Optimisation and Calculus of Variations4 (1999) 377-403. Zbl0978.53065MR1693912
- [6] Agrachev A.A, Bonnard B, Chyba M, Kupka I, Sub-Riemannian sphere in Martinet flat case, J. ESAIM: Control, Optimisation and Calculus of Variations2 (1997) 377-448. Zbl0902.53033MR1483765
- [7] Bellaïche A, The tangent space in sub-Riemannian geometry, in: Sub-Riemannian Geometry, Birkhäuser, 1996, pp. 1-78. Zbl0862.53031MR1421822
- [8] Bianchini R.M, Stefani G, Graded approximations and controllability along a trajectory, SIAM J. Control Optim.28 (1990) 903-924. Zbl0712.93005MR1051629
- [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. Zbl0929.53016
- [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. Zbl0988.35008MR1871126
- [11] Chow W.-L, Über Systeme von linearen partiellen Differentialgleichungen ester Ordnung, Math. Ann.117 (1939) 98-105. Zbl65.0398.01MR1880JFM65.0398.01
- [12] Filippov A.F, On certain questions in the theory of optimal control, Vestnik Moskov. Univ., Ser. Matem., Mekhan., Astron.2 (1959) 25-32. Zbl0090.06902
- [13] Gabrielov A, Projections of semi analytic sets, Funct. Anal. Appl.2 (1968) 282-291. Zbl0179.08503
- [14] Gauthier J.-P, Kupka I, Observability for systems with more outputs than inputs and asymptotic observers, Mathem. Zeitschrift223 (1996) 47-78. Zbl0863.93008MR1408862
- [15] Ge Zhong, Horizontal path space and Carnot–Caratheodory metric, Pacific J. Math.161 (1993) 255-286. Zbl0797.49033
- [16] Hironaka H, Subanalytic sets, in: Numbers Theory, Algebraic Geometry, and Commutative Algebra (in honor of V. Akizuki), Tokyo, 1973, pp. 453-493. Zbl0297.32008MR377101
- [17] Jacquet S, Subanalyticity of the sub-Riemannian distance, J. Dynamical and Control Systems5 (1999). Zbl0963.53014MR1706801
- [18] Rashevsky P.K, About connecting two points of a completely nonholonomic space by admissible curve, Uch. Zapiski Ped. Inst. Libknechta2 (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. Zbl0603.93006MR935375
- [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. Zbl0772.49019MR1184651
- [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 Iberoamericana2 (3) (1986) 307-317. Zbl0638.49018MR908055
- [23] Tamm M, Subanalytic sets in the calculus of variations, Acta Mathematica46 (1981) 167-199. Zbl0478.58010MR611382
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