Stochastic control in a determinate differential pursuit-evasion game

Abstract

In the paper, on the material of originally determinate differential game on minimax-maximin time up to the encounter of the controlled object with the wanted target is discussed a formalization, on which the theory of probabilities plays an important role. We tracked the way from descriptive theorems of existence of a price and saddle point in the original game to the principal result, namely, formation of approximation minimax and maximin controls on the basis of stochastic guides in feedback circuits.