Free Access
Issue
ESAIM: COCV
Volume 19, Number 1, January-March 2013
Page(s) 274 - 287
DOI https://doi.org/10.1051/cocv/2012006
Published online 12 June 2012
  1. A. Agrachev and R.V. Gamkrelidze, Second order optimality condition for the time optimal problem. Matem. Sbornik 100 (1976) 610–643. [Google Scholar]
  2. A. Agrachev and R.V. Gamkrelidze, Symplectic methods for optimization and control, in Geometry of Feedback and Optimal Control, edited by B. Jacubczyk and W. Respondek. Marcel Dekker, New York (1997). [Google Scholar]
  3. A. Agrachev and J.-P. Gauthier, On subanalyticity of Carnot-Carathéodory distances. Ann. Inst. Henri Poincaré Anal. Non Linéaire 18 (2001) 359–382. [CrossRef] [Google Scholar]
  4. A. Agrachev and Y. Sachkov, Control Theory from the Geometric Viewpoint, edited by Springer. Encycl. Math. Sci. 87 (2004). [Google Scholar]
  5. A. Agrachev and A. Sarychev, Abnormal sub-Riemannian geodesics : morse index and rigidity. Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 635–690. [Google Scholar]
  6. A. Agrachev and A. Sarychev, On abnormal extremals for Lagrange variational problems. J. Math. Syst. Estim. Control 8 (1998) 87–118. [Google Scholar]
  7. A. Agrachev and A. Sarychev, Sub-Riemannian metrics : minimality of abnormal geodesics versus sub-analyticity. ESAIM : COCV 4 (1999) 377–403. [CrossRef] [EDP Sciences] [Google Scholar]
  8. A. Agrachev, B. Bonnard, M. Chyba and I. Kupka, Subriemannian sphere in martinet flat case. ESAIM : COCV 2 (1997) 377–448. [Google Scholar]
  9. A. Bellaïche, The tangent space in sub-Riemannian geometry. Sub-Riemannian Geometry, Progr. Math. 144 (1996) 1–78. [Google Scholar]
  10. J.-M. Bismut, Large deviations and the Malliavin calculus, Progr. Math. 45 (1984). [Google Scholar]
  11. G.A. Bliss, Lectures on the calculus of variations. University of Chicago Press (1946). [Google Scholar]
  12. B. Bonnard and M. Chyba, Singular Trajectories and Their Role in Control Theory. Springer, Berlin (2003). [Google Scholar]
  13. R.L. Bryant and L. Hsu, Rigidity of integral curves of rank 2 distributions. Invent. Math. 114 (1993) 435–461. [CrossRef] [MathSciNet] [Google Scholar]
  14. G. Buttazzo, M. Giaquinta and S. Hildebrandt, One-dimensional variational problems. An introduction, Oxford Lecture Series. Edited by Univ. of Oxford Press, New-York. Math. App. 15 (1998). [Google Scholar]
  15. Y. Chitour, F. Jean and E. Trélat, Genericity results for singular curves. J. Differ. Geom. 73 (2006) 45–73. [Google Scholar]
  16. W.L. Chow, Über systeme von linearen partiellen differentialgleichungen erster Ordnung. Math. Ann. 117 (1940) 98–105. [CrossRef] [Google Scholar]
  17. B.S. Goh, Necessary conditions for singular extremals involving multiple control variables. SIAM J. Control 4 (1966) 716–731. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Golé and R. Karidi, A note on Carnot geodesics in nilpotent Lie groups. J. Dyn. Control Syst. 1 (1995) 535–549. [CrossRef] [Google Scholar]
  19. U. Hamenstädt, Some regularity theorems for Carnot-Carathéodory metrics. J. Differ. Geom. 32 (1990) 819–850. [Google Scholar]
  20. L. Hsu, Calculus of variations via the Griffiths formalism. J. Differ. Geom. 36 (1991) 551–591. [Google Scholar]
  21. S. Jacquet, Subanalyticity of the sub-Riemannian distance. J. Dyn. Control Syst. 5 (1999) 303–328. [CrossRef] [Google Scholar]
  22. G.P. Leonardi and R. Monti, End-point equations and regularity of sub-Riemannian geodesics. Geom. Funct. Anal. 18 (2008) 552–582. [CrossRef] [MathSciNet] [Google Scholar]
  23. W.S. Liu and H.J. Sussmann, Shortest paths for sub-Riemannian metrics of rank two distributions, edited by American Mathematical Society, Providence, RI. Mem. Amer. Math. Soc. 118 (1995) 104. [Google Scholar]
  24. J. Milnor, Morse Theory, edited by Princeton University Press, Princeton, New Jersey. Annals of Mathematics Studies 51 (1963). [Google Scholar]
  25. J. Mitchell, On Carnot-Carathéodory metrics. J. Differ. Geom. 21 (1985) 35–45. [Google Scholar]
  26. R. Montgomery, Abnormal minimizers. SIAM J. Control Optim. 32 (1994) 1605–1620. [CrossRef] [MathSciNet] [Google Scholar]
  27. R. Montgomery, A tour of subriemannian geometries, their geodesics and applications, edited by American Mathematical Society, Providence, RI. Mathematical Surveys and Monographs 91 (2002). [Google Scholar]
  28. B. O’Neill, Submersions and geodesics. Duke Math. J. 34 (1967) 363–373. [CrossRef] [MathSciNet] [Google Scholar]
  29. P.K. Rashevsky, About connecting two points of a completely nonholonomic space by admissible curve. Uch. Zapiski Ped. Inst. Libknechta 2 (1938) 83–94. [Google Scholar]
  30. R.S. Strichartz, Sub-Riemannian geometry. J. Differ. Geom. 24 (1986) 221–263. [Corrections to Sub-Riemannian geometry. J. Differ. Geom. 30 (1989) 595–596]. [Google Scholar]
  31. V.S. Varadarajan, Lie groups, Lie algebras and their representation. Springer-Verlag, New York (1984). [Google Scholar]
  32. L.C. Young, Lectures on the calculus of variations and optimal control theory. W.B. Saunders Co., Philadelphia-London-Toronto, Ont. (1969). [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.