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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 publié
Date
1979
Journal name
Journal of Optimization Theory and Applications
Volume
27
Number
1
Publisher
Springer
Pages
51-69
Publication identifier
Metadata
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Author(s)
Bernhard, Pierre
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.
Subjects / Keywords
Linear differential games; conjugate points; saddle points