Setting and Solving of the Game Problem of Confrontation of the Hardware-Redundant Dynamic System with an Attacking Enemy Operating in the Conflict Process in Conditions of Incomplete Information

Abstract

The game task of confrontation of the attacked hardware-redundant dynamic system with an attacking enemy operating in conditions of incomplete information about the behavior of the attacked enemy in a conflict was posed and solved numerically and analytically. The attacking party aspires to increase the intensity of failures of the components of the attacked system due to its attack resources, up to its total failure. The attacked party, due to the corresponding strategy of redistribution of the reserve units of the hardware-redundant dynamic system between the failed main units at the appropriate instants of time, strives to maximize the probability of a failure-free operation of the attacked system by the end of the confrontation (game) with the attacking enemy. Behavior of the system under attack in the process of a conflict is approximated by the Markov process, while the number of the operable states is equal to the number of the failed functional units, not exceeding the number of the standby units. As a function of the board in the considered game the probability of a failure-free operation of the attacked system is used by the time the game ends. The solution to the game is the vector of the system setup moments after the corresponding failures of the functional units and a set of the reservation vectors corresponding to the instantaneous settings of the attacked system, which maximize the probability of a system failure during a conflict. The differential game model is reduced to a multi-step matrix model with the given probabilities of the states of the attacking enemy. Numerical algorithms for calculation of the reservation vector for the attacked system are presented, which maximize the probability of its trouble-free operation by the end of the game and for solving of the game problem in a form convenient for its implementation on a personal computer.