Linear-quadratic, two-person, zero-sum differential games: Necessary and sufficient conditions
Bernhard, Pierre (1979), Linear-quadratic, two-person, zero-sum differential games: Necessary and sufficient conditions, Journal of Optimization Theory and Applications, 27, 1, p. 51-69. http://dx.doi.org/10.1007/BF00933325
Type
Article accepté pour publication ou publiéDate
1979Journal name
Journal of Optimization Theory and ApplicationsVolume
27Number
1Publisher
Springer
Pages
51-69
Publication identifier
Metadata
Show full item recordAuthor(s)
Bernhard, PierreAbstract (EN)
We consider linear-quadratic, two-person, zero-sum perfect information differential games, possibly with a linear target set. We show a necessary and sufficient condition for the existence of a saddle point, within a wide class of causal strategies (including, but not restricted to, pure state feedbacks). The main result is that, when they exist, the optimal strategies are pure feedbacks, given by the classical formulas suitably extended, and that existence may be obtained even in the presence of a conjugate point within the time interval, provided it is of a special type that we call even.Subjects / Keywords
Linear differential games; conjugate points; saddle pointsRelated items
Showing items related by title and author.
-
Bernhard, Pierre (1980) Article accepté pour publication ou publié
-
Cardaliaguet, Pierre; Laraki, Rida; Sorin, Sylvain (2012) Article accepté pour publication ou publié
-
Vigeral, Guillaume; Sorin, Sylvain (2013) Article accepté pour publication ou publié
-
Rochet, Jean-Charles (1987) Article accepté pour publication ou publié
-
Vigeral, Guillaume (2012) Document de travail / Working paper