Numeric Study of Problem “Attacker – Defender – Target” in the Framework of Zero-Sum Differential Games

In the line, an “attacker – defender – target” game is considered. All objects have linear dynamics of a general type and geometric constraints for their controls. The attacker minimizes the distance between it and the target at some instant. With that, it must provide at some earlier instant that the distance between it and the defender is not less than some given threshold. Such a formulation corresponds to a problem of a space intercept when all objects have high velocities, which are almost parallel to the initial lines-of-sight attacker – target and attacker – defender. By means of the standard change of variables, the game can be transformed to an equivalent two-dimenesional zero-sum differential game. In the talk, the authors demonstrate numerically constructed maximal stable bridges (solvability sets) for different variants of the game parameters. The used geometric algorithm for constructing maximal stable bridges is discussed.