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Linear-quadratic, two-person, zero-sum differential games: Necessary and sufficient conditions

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Date
1979
Dewey
Probabilités et mathématiques appliquées
Sujet
Linear differential games; conjugate points; saddle points
Journal issue
Journal of Optimization Theory and Applications
Volume
27
Number
1
Publication date
1979
Article pages
51-69
Publisher
Springer
DOI
http://dx.doi.org/10.1007/BF00933325
URI
https://basepub.dauphine.fr/handle/123456789/13204
Collections
  • CEREMADE : Publications
Metadata
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Author
Bernhard, Pierre
Type
Article accepté pour publication ou publié
Abstract (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.

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