Setting and solving the game confrontation problem of the hardware-redundant dynamic system with an attacking enemy operating under incomplete information in the conflict process

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