On the optimal control of implicit systems

Philippe Petit

ESAIM: Control, Optimisation and Calculus of Variations (1998)

  • Volume: 3, page 49-81
  • ISSN: 1292-8119

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Petit, Philippe. "On the optimal control of implicit systems." ESAIM: Control, Optimisation and Calculus of Variations 3 (1998): 49-81. <http://eudml.org/doc/90533>.

@article{Petit1998,
author = {Petit, Philippe},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {optimal control; --submanifolds; implicit differential equations},
language = {eng},
pages = {49-81},
publisher = {EDP Sciences},
title = {On the optimal control of implicit systems},
url = {http://eudml.org/doc/90533},
volume = {3},
year = {1998},
}

TY - JOUR
AU - Petit, Philippe
TI - On the optimal control of implicit systems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 1998
PB - EDP Sciences
VL - 3
SP - 49
EP - 81
LA - eng
KW - optimal control; --submanifolds; implicit differential equations
UR - http://eudml.org/doc/90533
ER -

References

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  1. [1] V. Alexeev, V.E. Galeev, V. Tikhomirov: Recueil de problèmes d'optimisation, Mir, Moscou, 1987. 
  2. [2] V. Alexeev, V. Tikhomirov, S. Fomin: Optimal control, Plenum Publishing Corporation, New York, 1987. Zbl0689.49001
  3. [3] G.A. Bliss: The problem of Lagrange in the calculus of variations, American Journal of Mathematics 52 ( 1930), 673-744. Zbl56.0435.01MR1506783JFM56.0435.01
  4. [4] G.A. Bliss: Lectures on the calculus of variations, University of Chicago press, Chicago, 1946. Zbl0063.00459MR17881
  5. [5] C. Carathéodory: Calculus of variations and partial differential equations of the first order, Series in Mathematical Physics, Holden-Day, San francisco, Cambridge, London, Amsterdam, 1967. Zbl0134.31004MR232264
  6. [6] E. Cartan: Sur l'intégration de certains systèmes indéterminés d'équations différentielles, vol. 2, CNRS, Paris, 1984. 
  7. [7] L. Cesari: Optimization-theory and applications, Applications of Mathematics, Springer-Verlag, New York Heidelberg Berlin, 1983. Zbl0506.49001MR688142
  8. [8] F. Clarke: Optimization and nonsmooth analysis, Les publications du Centre de Recherche Mathématiques de l'Université de Montréal, 1989. Zbl0727.90045MR1019086
  9. [9] J. Dieudonné: Eléments d'analyse, vol. 3, Gauthier-Villars, Paris, 1970. Zbl0208.31802MR270377
  10. [10] P.A. Griffiths: Exterior differential systems and the calculus of variations, Birkäuser, Boston, 1983. Zbl0512.49003MR684663
  11. [11] J. Hadamard: Leçons sur le calcul des variations, Herman, Paris, 1940. JFM41.0432.02
  12. [12] V. Jurdjevic: Geometric control theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1997. Zbl0940.93005MR1425878
  13. [13] Ph. Loewen: Optimal control via nonsmooth analysis, CRM Proceedings and Lecture Notes, vol. 2, American Mathematical Society, Providence, Rhode Island USA, 1993. Zbl0874.49002MR1232864
  14. [14] L. Pontryagin et al.: Théorie mathématique de processus optimaux, Mir, Moscou, 1974. MR358482
  15. [15] P.-J. Rabier, W.C. Rheinboldt: A general existence and uniqueness theory for implicit differential-algebraic equations, Differential Integral Equations 4 ( 1991), 563-582. Zbl0722.34004MR1097919
  16. [16] P.-J. Rabier, W.C. Rheinboldt: A geometric treatment of implicit differential-algebraic equations, Journal of Differential Equations 109 ( 1994), 110-146. Zbl0804.34004MR1272402

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