Some algorithms for differential games with two players and one target

P. Cardaliaguet; M. Quincampoix; P. Saint-Pierre

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (1994)

  • Volume: 28, Issue: 4, page 441-461
  • ISSN: 0764-583X

How to cite

top

Cardaliaguet, P., Quincampoix, M., and Saint-Pierre, P.. "Some algorithms for differential games with two players and one target." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 28.4 (1994): 441-461. <http://eudml.org/doc/193747>.

@article{Cardaliaguet1994,
author = {Cardaliaguet, P., Quincampoix, M., Saint-Pierre, P.},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {victory domains of a differential game; convergence results},
language = {eng},
number = {4},
pages = {441-461},
publisher = {Dunod},
title = {Some algorithms for differential games with two players and one target},
url = {http://eudml.org/doc/193747},
volume = {28},
year = {1994},
}

TY - JOUR
AU - Cardaliaguet, P.
AU - Quincampoix, M.
AU - Saint-Pierre, P.
TI - Some algorithms for differential games with two players and one target
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 1994
PB - Dunod
VL - 28
IS - 4
SP - 441
EP - 461
LA - eng
KW - victory domains of a differential game; convergence results
UR - http://eudml.org/doc/193747
ER -

References

top
  1. [1] J.-P. AUBIN, 1989, Victory and defeat in differential games, Lecture notes in Control and Information Sciences, 121, 337-347, Springer-Verlag, New York, Berlin, 1989. Zbl0682.90107MR1231129
  2. [2] J.-P. AUBIN, H. FRANKOWSKA, 1991, Set-valued analysis, Birkhäuser. Zbl0713.49021MR1048347
  3. [3] J.-P. AUBIN, 1992, Viability Theory, Birkhäuser. Zbl0755.93003MR1134779
  4. [4] P. BERNHARD, 1979, Contribution à l'étude des jeux à information parfaite et à somme nulle, Thèse de Doctorat d'Etat, Paris VI. 
  5. [5] P. BERNHARD P., B. LARROUTUROU, 1989, Etude de la barrière pour un problème de fuite optimale dans le plan, preprint, Rapport de recherche de l'INRIA, Le Chesnay, France. Zbl0737.90088
  6. [6] P. CARDALIAGUET (Submitted), Discriminating and leadership domains. 
  7. [7] P. CARDALIAGUET (Submitted), The target problem for nonanticipative strategies. 
  8. [8] N. J. ELLIOT, N. J. KALTON, 1972, The existence of value in differential games, Mem. Amer. Math. Soc., 126. Zbl0262.90076MR359845
  9. [9] L. C. EVANS, P. E. SOUGANIDIS, 1984, Differential games and representation formulas for solutions of Hamilton-Jacobi Equations, Transactions of A.M.S., 282, 487-502. 
  10. [10] H. FRANKOWSKA, M. QUINCAMPOIX, 1991, Viability kernels of differential inclusions with constraints : Algorithm and applications, J. Math, of Systems, Estimation and Control, 1, No. 3, 371-388. Zbl0719.58007MR1151310
  11. [11] H. FRANKOWSKA, M. QUINCAMPOIX, 1992, Isaacs' equations for value-functions of differential games, International Series of Numerical Mathematics, 107, Birkhäuser Verlag Basel. Zbl0770.90093MR1223370
  12. [12] R. ISAACS, 1965, Differential Games, Wiley, New York. Zbl0125.38001MR210469
  13. [13] N. N. KRASOVSKII, A. I. SUBBOTIN, 1988, Game-Theorical Control Problems, Springer-Verlag, New York. Zbl0649.90101MR918771
  14. [14] V. LAPORTE, J. M. NICOLAS, P. BERNHARD, 1990, About the resolution of discrete pursuit games and its applications to naval warfare, Proceedings of the International Symposium on differential games and applications, Helsinki. Zbl0831.90143MR1179875
  15. [15] N. S. PONTRYAGIN, 1968, Linear differential games I and II, Soviet Math. Doklady, 8, (3 & 4) 769-771, 910-912. Zbl0157.16401
  16. [16] M. QUINCAMPOIX, 1991, Playable Differential Games, J. Math. Analysis and Appl., 161, No. 1, 194-211. Zbl0747.90123MR1127557
  17. [17] M. QUINCAMPOIX, 1992, Differential Inclusions and Target Problems, SIAM J. Control and Optimization, 30, No. 2, 324-335. Zbl0862.49006MR1149071
  18. [18] M. QUINCAMPOIX (to appear), Invariance envelopes and invariance kernels for Lipschitzean differential Inclusions, Proceedings of conference on Differential Inclusions and set-valued analysis, Pamporovo, September 1990. Zbl0794.49005MR1075661
  19. [19] M. QUINCAMPOIX, P. SAINT-PIERRE (to appear), An algorithm for Viability Kernels in Hölderian case : Approximation by Discrete Viability Kernels, J. Math. of Systems, Estimation and Control. Zbl0831.34016
  20. [20] P. SAINT-PIERRE (to appear), Approximation of the Viability Kernel, in Applied Mathematics & Optimisation. Zbl0790.65081MR1254059
  21. [21] P. VARAIYA, 1971, Differential games with dynamical systems, in Differential games and related topics, Kuhn & Szego editors, North-Holland. Zbl0266.90070MR278760

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.