Generic properties of singular trajectories

B. Bonnard; I. Kupka

Annales de l'I.H.P. Analyse non linéaire (1997)

  • Volume: 14, Issue: 2, page 167-186
  • ISSN: 0294-1449

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Bonnard, B., and Kupka, I.. "Generic properties of singular trajectories." Annales de l'I.H.P. Analyse non linéaire 14.2 (1997): 167-186. <http://eudml.org/doc/78407>.

@article{Bonnard1997,
author = {Bonnard, B., Kupka, I.},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear systems; optimal control; singular extremals; generic properties; minimum order},
language = {eng},
number = {2},
pages = {167-186},
publisher = {Gauthier-Villars},
title = {Generic properties of singular trajectories},
url = {http://eudml.org/doc/78407},
volume = {14},
year = {1997},
}

TY - JOUR
AU - Bonnard, B.
AU - Kupka, I.
TI - Generic properties of singular trajectories
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 1997
PB - Gauthier-Villars
VL - 14
IS - 2
SP - 167
EP - 186
LA - eng
KW - nonlinear systems; optimal control; singular extremals; generic properties; minimum order
UR - http://eudml.org/doc/78407
ER -

References

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  1. [BR] R. Benedetti and J.J. Risler, Real algebraic and semi-algebraic sets, Hermann, Paris, 1990. Zbl0694.14006MR1070358
  2. [B1] B. Bonnard, On singular extremals in the time minimal control problem in R3, SIAM J. on Control and Optimization, Vol. 23, No. 5, 1985, pp. 794-802. Zbl0602.49027MR798060
  3. [B2] B. Bonnard, Feedback equivalence for nonlinear systems and the time optimal control problem, SIAM J. on Control and Optimization, Vol. 29, No. 6, 1991, pp. 1300-1321. Zbl0744.93033MR1132184
  4. [BK1] 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. Vol. 5, 1993, pp. 111-159. Zbl0779.49025MR1205250
  5. [BK2] B. Bonnard and I. Kupka, Deux propriétés génériques des trajectoires singulières, Note au C.R.A.S., t. 319, série I, 1994, pp. 509-512. Zbl0816.58013MR1296783
  6. [GG] M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Springer Verlag, New York, 1973. Zbl0294.58004MR341518
  7. [GP] M. Goreski and R. Mcpherson, Stratified Morse theory, Springer Verlag, New York, 1988. Zbl0639.14012MR932724
  8. [HT] M. Henneaux and C. Teitelboim, Quantization of gauge systems, Princeton University Press, 1992. Zbl0838.53053MR1191617
  9. [L] C. Lobry, Une propriété générique des couples de champs de vecteur, Czech. Math. J., Vol. 22, (97), 1972, pp. 230-237. Zbl0242.58007MR300305
  10. [Pa] L. Pontriaguine et al., Théorie mathématique des processus optimaux, Editions Mir, Moscou, 1974. Zbl0289.49002MR358482

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