Extremal aiming and extremal displacement in a game-theoretical control. (English) Zbl 0625.90104

Probl. Control Inf. Theory/Problemy Upravl. Teor. Inform. 13 (1984), No. 5, 287-302 (1984).
As the author has proved in his joint book with A. N. Subbotin [“Differential games”, French translation (1977; Zbl 0383.90111)] control problems with incomplete information can be formalized within the framework of the theory of differential games.
Introducing the concepts of “extremal aiming” and “extremal displacement”, it is proved in this paper that it is possible in some cases to calculate the game value and to determine the optimal strategies. In this way, a stochastic program synthesis for a general evolutionary system can be formulated. An illustrative problem, in which general aspects are analyzed in a concrete form, is given.


91A23 Differential games (aspects of game theory)
91A99 Game theory