Chikrii G. Role of information in the game dynamic problems

The quasilinear conflict-controlled processes are analyzed with help of the positional approach. Sufficient conditions for hitting a terminal set of cylindrical form in the "first absorption time" are obtained. The conditions are specified for a wide range of functional-differential systems. On the basis of the method of resolving functions, schemes of the group pursuit are developed in the case of difference-differential systems with delay. The method of matrix resolving functions is created to study dynamic games. Comparison of guaranteed times of the method different schemes is performed. It is shown that the linear game of approach with delay of information can be reduced to certain perfect information game. This makes it feasible to apply all known methods to solve the former. The principle of time dilatation is developed to study differential games for which Pontryagin's condition fails. Sufficient conditions for collision avoidance are derived for the linear problem under state constraints, the nonlinear problem of avoidance a solid terminal set as well as the difference-differential game of avoidance a linear subspace. Necessary conditions for the time optimality of search for a stationary target are established.