Free Access
Volume 12, Number 3, July 2006
Page(s) 409 - 441
DOI https://doi.org/10.1051/cocv:2006007
Published online 20 June 2006
  1. J.F. Adams, Lectures on Lie groups. W.A. Benjamin, Inc., New York-Amsterdam (1969).
  2. A.A. Agrachev, Introduction to optimal control theory, in Mathematical control theory, Part 1, 2 (Trieste, 2001), ICTP Lect. Notes, VIII, Abdus Salam Int. Cent. Theoret. Phys., Trieste (2002) 453–513 (electronic).
  3. A.A. Agrachev and Y.L. Sachkov, Control theory from the geometric viewpoint, Encyclopaedia of Mathematical Sciences. 87 Springer-Verlag, Berlin (2004). Control Theory and Optimization, II.
  4. A.O. Barut and R. Raczka, Theory of group representations and applications. World Scientific Publishing Co., Singapore, second edn. (1986).
  5. B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Systèmes de champs de vecteurs transitifs sur les groupes de Lie semi-simples et leurs espaces homogènes, in Systems analysis (Conf., Bordeaux, 1978) 75 Astérisque, Soc. Math. France, Paris (1980) 19–45.
  6. B. Bonnard, V. Jurdjevic, I. Kupka and G. Sallet, Transitivity of families of invariant vector fields on the semidirect products of Lie groups. Trans. Amer. Math. Soc. 271 (1982) 525–535. [CrossRef] [MathSciNet]
  7. B. Bonnard, Couples de générateurs de certaines sous-algèbres de Lie de l'algèbre de Lie symplectique affine, et applications. Publ. Dép. Math. (Lyon) 15 (1978) 1–36.
  8. B. Bonnard, Contrôlabilité de systèmes mécaniques sur les groupes de Lie. SIAM J. Control Optim. 22 (1984) 711–722. [CrossRef] [MathSciNet]
  9. U. Boscain, T. Chambrion and J.-P. Gauthier, On the K + P problem for a three-level quantum system: optimality implies resonance. J. Dynam. Control Syst. 8 (2002) 547–572. [CrossRef]
  10. U. Boscain, G. Charlot and J.-P. Gauthier, Optimal control of the Schrödinger equation with two or three levels, in Nonlinear and adaptive control (Sheffield 2001), Springer, Berlin, Lect. Not. Control Inform. Sci. 281 (2003) 33–43.
  11. U. Boscain, G. Charlot, J.-P. Gauthier, S. Guérin and H.-R. Jauslin, Optimal control in laser-induced population transfer for two- and three-level quantum systems. J. Math. Phys. 43 (2002) 2107–2132. [CrossRef] [MathSciNet]
  12. U. Boscain and G. Charlot, Resonance of minimizers for n-level quantum systems with an arbitrary cost. ESAIM: COCV 10 (2004) 593–614. [CrossRef] [EDP Sciences]
  13. U. Boscain and Y. Chitour, On the minimum time problem for driftless left-invariant control systems on SO(2). Commun. Pure Appl. Anal. 1 (2002) 285–312. [CrossRef] [MathSciNet]
  14. R. Brockett, New issues in the mathematics of control, in Mathematics unlimited — 2001 and beyond. Springer, Berlin (2001), pp. 189–219.
  15. D. D'Allessandro and M. Dahleh, Optimal control of two-level quantum systems. IEEE Trans. Automat. Control 46 (2001) 866–876. [CrossRef] [MathSciNet]
  16. M.P. do Carmo, Riemannian geometry, Mathematics: Theory & Applications. Birkhäuser Boston Inc., Boston, MA (1992). Translated from the second Portuguese edition by Francis Flaherty.
  17. R. El Assoudi and J.-P. Gauthier, Controllability of right invariant systems on real simple Lie groups of type F4, G2, Cn, and Bn. Math. Control Signals Syst. 1 (1988) 293–301.
  18. R. El Assoudi and J.-P. Gauthier, Controllability of right-invariant systems on semi-simple Lie groups, in New trends in nonlinear control theory (Nantes, 1988). Springer, Berlin, Lect. Notes Control Inform. Sci. 122 (1989) 54–64.
  19. R. El Assoudi, J.P. Gauthier and I.A.K. Kupka, Controllability of right invariant systems on semi-simple Lie groups, in Geometry in nonlinear control and differential inclusions (Warsaw, 1993). Banach Center Publ., Polish Acad. Sci., Warsaw 32 (1995) 199–208.
  20. R. El Assoudi, J.P. Gauthier and I.A.K. Kupka, On subsemigroups of semisimple Lie groups. Ann. Inst. H. Poincaré Anal. Non Linéaire 13 (1996) 117–133.
  21. R. El Assoudi and J.-P. Gauthier, Contrôlabilité sur l'espace quotient d'un groupe de Lie par un sous-groupe compact. C. R. Acad. Sci. Paris Sér. I Math. 311 (1990) 189–191.
  22. A.L. Fradkov and A.N Churilov, Eds. Proceedings of the conference “Physics and Control” 2003 IEEE. August (2003).
  23. J.-P. Gauthier, I. Kupka and G. Sallet, Controllability of right invariant systems on real simple Lie groups. Syst. Contr. Lett. 5 187–190 (1984).
  24. S. Helgason, Differential geometry, Lie groups, and symmetric spaces 80, Pure Appl. Math., Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York (1978).
  25. V. Jurdjevic, Optimal control problems on Lie groups: crossroads between geometry and mechanics, in Geometry of feedback and optimal control. Dekker, New York, Monogr. Textbooks Pure Appl. Math. 207 (1998) 257–303.
  26. V. Jurdjevic, Optimal control, geometry, and mechanics, in Mathematical control theory. Springer, New York (1999) 227–267.
  27. V. Jurdjevic and I. Kupka, Control systems on semisimple Lie groups and their homogeneous spaces. Ann. Inst. Fourier (Grenoble) 31 (1981) 151–179. [MathSciNet]
  28. V. Jurdjevic and I. Kupka, Control systems subordinated to a group action: accessibility. J. Differ. Equ. 39 (1981) 186–211. [CrossRef]
  29. V. Jurdjevic, Geometric control theory, Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge 52 (1997).
  30. V. Jurdjevic, Lie determined systems and optimal problems with symmetries, in Geometric control and non-holonomic mechanics (Mexico City, 1996), Providence, RI. CMS Conf. Proc., Amer. Math. Soc. 25 (1998) 1–28.
  31. A. Katok and B. Hasselblatt, Introduction to the modern theory of dynamical systems, Encyclopedia of Mathematics and its Applications. 54 Cambridge University Press, Cambridge (1995). With a supplementary chapter by Katok and Leonardo Mendoza.
  32. N. Khaneja, S.J. Glaser and R. Brockett, Sub-Riemannian geometry and time optimal control of three spin systems: quantum gates and coherence transfer. Phys. Rev. A 65 (2002) 032301, 11. [CrossRef] [MathSciNet]
  33. I. Kupka, Applications of semigroups to geometric control theory, in The analytical and topological theory of semigroups de Gruyter Exp. Math. de Gruyter, Berlin 1 (1990) 337–345.
  34. J. Milnor, Morse theory. Based on lecture notes by M. Spivak and R. Wells. Annals of Mathematics Studies, No. 51. Princeton University Press, Princeton, N.J. (1963).
  35. J. Milnor, Curvatures of left invariant metrics on Lie groups. Advances Math. 21 (1976) 293–329. [CrossRef]
  36. T. Püttmann, Injectivity radius and diameter of the manifolds of flags in the projective planes. Math. Z. 246 (2004) 795–809. [CrossRef] [MathSciNet]
  37. Y.L. Sachkov, Controllability of invariant systems on Lie groups and homogeneous spaces. J. Math. Sci. 100 (2000) 2355–2427 Dynamical systems, 8.
  38. H.J. Sussmann and V. Jurdjevic, Controllability of nonlinear systems. J. Differ. Equ. 12 (1972) 95–116. [CrossRef]
  39. V.S. Varadarajan, Lie groups, Lie algebras, and their representations. Prentice-Hall Inc., Englewood Cliffs, N.J. (1974). Prentice-Hall Series in Modern Analysis.

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.