Control design in problems with an unknown level of dynamic disturbance

Linear differential games for two players with a fixed termination time are considered. The objective of player 1 is to bring the motion of the system into an assigned terminal set or fairly close to it at the termination time. Player 2 (the disturbance) opposes this. The control of player 1 is scalar and its absolute value is subject to a constraint. One special feature of the formulation is that no constraint on the control of player 2 is specified a priori. A method of designing the feedback control of player 1 that works satisfactorily over a broad range of disturbance levels and corresponds to a small magnitude of the control input at a low level of disturbance is proposed and verified. A numerical program is written for the case of small dimensionality of the phase variable. The results of the simulation of a system that describes a conflict-controlled pendulum are presented.