Extremum Strategies of Approach of Controlled Objects in Dynamic Game Problems with Terminal Payoff Function

Cybernetics and Systems Analysis - The authors propose a method for solving the problem of approach of controlled objects in dynamic game problems with a terminal payoff function. The method is...     

The analytical method to solve nonstationary differential games of pursuit

The game problem of pursuit is studied for dynamic processes evolving under uncertainty and counteraction. The terminal set is supposed to be a cylindrical set-valued mapping. The method of resolving functions is used to establish the sufficient conditions for the game termination in the class of quasi- and stroboscopic strategies for various schemes of the method. The guaranteed times are compared. The results are illustrated using the model with integral control unit and game problems with simple motion.     

Solving the dynamic traveling salesman game problem

A game problem of the successive capture of a team of evaders by a single pursuer under conditions of “simple motions” of the players is analyzed. The performance criterion is the total time all the evaders are captured. It is assumed that the pursuer is guided by the parallel pursuit law. In such a case, the optimal response of the evaders is the straightforward motion with maximum speed. The original infinite-dimensional problem can therefore be reduced to two finite-dimensional problems.     

Lower semicontinuous dependences in differential pursuit and evasion games

Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 96–108, July–August, 1995. Original     

Comparison of guaranteed times in conflict-controlled motion

The paper proposes a modified scheme of the method of resolving functions for conflict-controlled processes with a cylindrical terminal set. This scheme ensures that the game is terminated in a definite guaranteed time in the class of stroboscopic strategies without any additional conditions. The guaranteed times of various schemes of the method of resolving functions are compared with that of the first Pontryagin method in terms of convex-valued mappings for a certain structure of the terminal set. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 4, pp. 89–100, July–August 2008.     

Extremal selectors in differential pursuit games. II

We establish sufficient conditions on the parameters of a conflict-controlled process, the initial position, and the selectors which ensure that the Pontryagin method and the decision function method produce different pursuit times.Part I seeKibernetika, No. 6 (1988).Translated from Kibernetika, No. 2, pp. 47–53, 64, March–April, 1989.     

Simple pursuit of one evader by a group

The pursuit of one evader by a group of controlled pursuers is considered for the case of simple motion of the players in nonempty compact sets. Sufficient solvability conditions are derived. These conditions are sometimes also necessary.Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 131–137, May–June, 1992.