On one conflict control problem with imperfect delayed information

For a conflict-controlled dynamical system, we consider the problem of optimal feedback control with imperfect information about dynamic disturbance and with imperfect delayed information about values of a phase variable that characterizes the current state of the system. The problem is formalized as a two-player antagonistic differential game. In solving the problem, the method of program stochastic synthesis and the method of extremal shift to accompanying points are used. An optimal control strategy is established.