Titre du document / Document title

The one-dimensional projection method in an integrally-constrained linear game and single-type games

Auteur(s) / Author(s)

UKHOBOTOV V. I. ;

Résumé / Abstract

When one projects a simple-motion linear differential game the player vectorgrams in which are time-dependent symmetric compact sets on a one-dimensional subspace, one obtains a one-dimensional game, where the player vectorgrams are segments. The necessary and sufficient conditions for termination in the one-dimensional game will be the necessary conditions for termination in the original game. In some cases, they are also sufficient. The criterion for terminating, at a specified instant, a game in which the first player's choice of control is integrally constrained, where the player vectorgrams and the termination set are described by the same convex symmetric compact set, homothetically elongated, is proven. The values of the game cost are calculated for a payment equal to the value of the Minkowski function of this compact set when the constraints on the choice of the player controls are geometric and for an integral constraint on the first player's choice of control.

Revue / Journal Title

Journal of computer & system sciences international   ISSN 1064-2307 

Source / Source

1995, vol. 33, n^o5, pp. 123-130 (8 ref.)

Langue / Language

Anglais

Editeur / Publisher

MAIK Nauka/Interperiodica, Moscow, RUSSIE, FEDERATION DE  (1992) (Revue)

Mots-clés anglais / English Keywords

Differential game ; Projection method ; One dimensional model ; Linear game ; Game theory ; Minkowski metric ; Method study ; Attainable set ;

Mots-clés français / French Keywords

Jeu différentiel ; Méthode projection ; Modèle 1 dimension ; Jeu linéaire ; Théorie jeu ; Métrique Minkowski ; Etude méthode ; Ensemble atteignable ;

Mots-clés espagnols / Spanish Keywords

Juego diferencial ; Método proyección ; Modelo 1 dimensión ; Juego lineal ; Teoría juego ; Métrico Minkowski ; Estudio método ; Conjunto alcanzadizo ;

Localisation / Location

INIST-CNRS, Cote INIST : 11554, 35400005377149.0180