Weak evasion of a group of rigidly coordinated evaders in the nonlinear problem of group pursuit

A natural generalization of differential two-person games is conflict controlled processes with a group of controlled objects (from at least one of the conflicting sides). The problems of conflict interaction between two groups of controlled objects are the most difficult-to-research. The specificity of these problems requires new methods to study them. This paper deals with the nonlinear problem of pursuing a group of rigidly coordinated evaders (i.e. using the same control) by a group of pursuers under the condition that the maneuverability of evaders is higher. The goal of evaders is to ensure weak evasion for the whole group. By weak evasion we mean non-coincidence of geometrical coordinates, speeds, accelerations and so forth for the evader and all pursuers. The position control is constructed for all possible initial positions of the participants; this control guarantees a weak evasion for all evaders.