On guaranteeing point capture in linear n-on-1 endgame interception engagements with bounded controls

A linearized endgame interception scenario along a line between a single evading target and n pursuers is considered, in which the adversaries' controls are bounded and have arbitrary-order dynamics, and the evader's maneuvers are not known a priori to the pursuing team. To determine the merit in utilizing multiple interceptors, in terms of their capability to impose point capture, a capturability analysis is performed, presenting necessary and sufficient conditions for the feasibility of point capture for any admissible evader maneuver. It is shown that the pursuing team is capable of guaranteeing point capture if and only if it consists of at least one pursuer capable of independently imposing point capture. This requirement is independent of the number of pursuers, leading to the conclusion that it cannot be relaxed by increasing the number of interceptors or by any manner of cooperation, in terms of coordinated motion, between the pursuers.