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
TypeArticle accepté pour publication ou publié
Journal nameJournal of Optimization Theory and Applications
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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 / KeywordsLinear differential games; conjugate points; saddle points
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