On a programmed construction in a positional differential game

V. D. Batukhtin, A. G. Chentsov


Abstract: Given the system
$$ \frac{dx}{dt}=f(t,x,u,v),\qquad x(t_0)=x_0. $$
sufficient conditions are considered for solving the game problem of convergence by a prescribed instant of time under mixed strategies. A programmed construction on the basis of generalized controls-measures is used to solve the problem. Necessary conditions for optimality of the programmed controls are studied.
Bibliography: 9 titles.

UDC: 518.9

MSC: Primary 90D25, 49B10; Secondary 49B40

Received: 19.04.1974

 English version: Mathematics of the USSR-Izvestiya, 1975, 9:4, 877–886

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