Free Access
Issue
ESAIM: COCV
Volume 6, 2001
Page(s) 387 - 414
DOI https://doi.org/10.1051/cocv:2001115
Published online 15 August 2002
  1. A. Agrachev, Compactness for sub-Riemannian length minimizers and subanalyticity. Rend. Sem. Mat. Torino 56 (1998). [Google Scholar]
  2. A. Agrachev, Quadratic mappings in geometric control theory. J. Soviet Math. 51 (1990) 2667-2734. [CrossRef] [Google Scholar]
  3. A. Agrachev, Any smooth simple H1-local length minimizer in the Carnot-Caratheodory space is a C0-local length minimizer, Preprint. Labo. de Topologie, Dijon (1996). [Google Scholar]
  4. A. Agrachev and A.V. Sarychev, Strong minimality of abnormal geodesics for 2-distributions. J. Dynam. Control Systems 1 (1995) 139-176. [CrossRef] [MathSciNet] [Google Scholar]
  5. A. Agrachev and A.V. Sarychev, Abnormal sub-Riemannian geodesics: Morse index and rigidity. Ann. Inst. H. Poincaré 13 (1996) 635-690. [Google Scholar]
  6. A. Agrachev and A.V. Sarychev, On abnormal extremals for Lagrange variational problems. J. Math. Systems Estim. Control 8 (1998) 87-118. [MathSciNet] [Google Scholar]
  7. G.A. Bliss, Lectures on the calculus of variations. U. of Chicago Press (1946). [Google Scholar]
  8. B. Bonnard and M. Chyba, The role of singular trajectories in control theory. Springer Verlag, Math. Monograph (to be published). [Google Scholar]
  9. B. Bonnard and I. Kupka, Théorie des singularités de l'application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal. Forum Math. 5 (1993) 111-159. [CrossRef] [MathSciNet] [Google Scholar]
  10. B. Bonnard and I. Kupka, Generic properties of singular trajectories. Ann. Inst. H. Poincaré Anal. Non Linéaire 14 (1997) 167-186. [CrossRef] [MathSciNet] [Google Scholar]
  11. B. Bonnard and E. Trélat, On the role of abnormal minimizers in SR-geometry, Preprint. Labo. Topologie Dijon. Ann. Fac. Sci. Toulouse (to be published). [Google Scholar]
  12. B. Bonnard and E. Trélat, Stratification du secteur anormal dans la sphère de Martinet de petit rayon, edited by A. Isidori, F. Lamnabhi Lagarrigue and W. Respondek. Springer, Lecture Notes in Control and Inform. Sci. 259, Nonlinear Control in the Year 2000, Vol. 2. Springer (2000). [Google Scholar]
  13. H. Brezis, Analyse fonctionnelle. Masson (1993). [Google Scholar]
  14. R.L. Bryant and L. Hsu, Rigidity of integral curves of rank 2 distributions. Invent. Math. 114 (1993) 435-461. [CrossRef] [MathSciNet] [Google Scholar]
  15. M.R. Hestenes, Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. Pacific J. Math. 1 (1951) 525-581. [CrossRef] [MathSciNet] [Google Scholar]
  16. E.B. Lee and L. Markus, Foundations of optimal control theory. John Wiley, New York (1967). [Google Scholar]
  17. C. Lesiak and A.J. Krener, The existence and Uniqueness of Volterra Series for Nonlinear Systems. IEEE Trans. Automat. Control AC 23 (1978). [Google Scholar]
  18. W.S. Liu and H.J. Sussmann, Shortest paths for sub-Riemannian metrics of rank two distributions. Mem. Amer. Math. Soc. 118 (1995). [Google Scholar]
  19. R. Montgomery, Abnormal minimizers. SIAM J. Control Optim. 32 (1997) 1605-1620. [CrossRef] [MathSciNet] [Google Scholar]
  20. M.A. Naimark, Linear differential operators. Frederick U. Pub. Co (1967). [Google Scholar]
  21. L. Pontryagin et al., Théorie mathématique des processus optimaux. Eds Mir, Moscou (1974). [Google Scholar]
  22. A.V. Sarychev, The index of the second variation of a control system. Math. USSR Sbornik 41 (1982). [Google Scholar]
  23. E. Trélat, Some properties of the value function and its level sets for affine control systems with quadratic cost. J. Dynam. Control Systems 6 (2000) 511-541. [CrossRef] [MathSciNet] [Google Scholar]
  24. E. Trélat, Étude asymptotique et transcendance de la fonction valeur en contrôle optimal ; catégorie log-exp dans le cas sous-Riemannien de Martinet, Ph.D. Thesis. Université de Bourgogne, Dijon, France (2000). [Google Scholar]
  25. Zhong Ge, Horizontal path space and Carnot-Caratheodory metric. Pacific J. Math. 161 (1993) 255-286. [MathSciNet] [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.