Couples de générateurs de certaines sous-algèbres de Lie de l'algèbre de Lie symplectique affine, et applications

 Access to full text

 Full (PDF)

1. 1 W. Boothby, A transitivity problem from control theory, J. Differential equations17, 296-307. (1975). Zbl0316.93006MR436210
2. 2 B. Bonnard, Controlabilité sur le groupe symplectique et couples de champs de vecteurs hamiltoniens contrôlables sur R2n, Thèse 3ème cycle - Metz (1978). 
3. 3 R.W. Brockett. System theory on group manifolds and coset spacesSiam J. Control (10) 2. 1972. Zbl0238.93001MR315559
4. 4 Ciampi, classical hamiltonian linear systems, Queen's papers in pure and applied mathematics, n° 31. Zbl0269.70013
5. 5 Gantmacher, Théorie des matrices, Tome 1, Dunod. Zbl0136.00410
6. 6 C. Godbillon, Géométrie différentielle et mécanique analytique, Hermann, Paris1969. Zbl0653.53001MR242081
7. 7 Helgason, Differential geometry and symmetric spaces, Academic Press1962. Zbl0111.18101MR145455
8. 8 N. Jacobson, Lie algebras, Interscience. Zbl0121.27504
9. 9 R. Hirschron, Controllability in nonlinear systems, J. Differential Equations19, 46-61 (1975). Zbl0315.93002MR431271
10. 10 R. Hirschron, Global controllability of nonlinear systems, Siam J. Control (1976). Zbl0341.93006MR304004
11. 11 V. Jurdjevic, H.J. Sussmann, Controllability of non linear systems, J. Differential Equations12, 95-116 (1972). Zbl0242.49040MR338882
12. 12 V. Jurdjevic, H.J. Sussmann, Control systems on Lie groups, J. Differential Equations12, 313-329 (1972). Zbl0237.93027MR331185
13. 13 I. Kupka, V. Jurdjevic, Conditions suffisantes d'accessibilité sur les groupes de Lie semi-simples. A paraître. 
14. 14 F.B. Lee, L. Markus, Foundations of optimal control theory, John Wiley and Sons (1967). Zbl0159.13201MR220537
15. 15 C. Lobry, Controlabilité des systèmes non linéaires, Siam J. control (8) 4 (1970). Zbl0207.15201
16. 16 C. Lobry, Controllability of non linear systems on compact manifolds, Siam J. Control (12) 4 (1974). Zbl0286.93006
17. 17 C. Lobry, Cours 3ème cycle. Bordeaux (1976). 
18. 18 G. Sallet, Couples de champs de vecteurs de Killing complètement contrôlables sur les sphères et espaces euclidiens, Thèse 3ème cycle, Metz (1976). 
19. 19 H.J. Sussmann, On the number of vector Fields needed to achieve controllability, Siam J. Control (13) 2 - 1975. Zbl0268.93006MR431267
20. 20 H.J. Sussmann, N. Levitt, On controllability by means of two vector Fields, Siam J. Control (13) 6 - 1975. Zbl0313.93006MR402812
21. 21 H.J. Sussmann, Some properties of vector Field systems that are not altered by small perturbations, J. Differential Equations, 20, 293-315 (1976). Zbl0346.49036MR394756

1. Andrei Agrachev, Thomas Chambrion, An estimation of the controllability time for single-input systems on compact Lie Groups