CONSTRUCTION OF THE VALUE FUNCTION IN A PURSUIT-EVASION GAME WITH 3 PURSUERS AND ONE EVADER

A differential pursuit-evasion game is considered with three pursuers and one evader. It is assumed that all objects (players) have simple m otions and that the game takes place in a plane. The control vectors s atisfy geometrical constraints and the evader has a superiority in con trol resources. The game time is fixed. The value functional is the di stance between the evader and the nearest pursuer at the end of the ga me. The problem of determining the value function of the game for any possible position is solved. Three possible cases for the relative arr angement of the players at an arbitrary time are studied: ''one-after- one'', ''two-after-one'', ''three-after-one-in-the-middle'' and ''thre e-after-one''. For each of the relative arrangements of the players a guaranteed result function is constructed. In the first three cases th e function is expressed analytically. In the fourth case a piecewise-p rogrammed construction is presented with one switchover, on the basis of which the value of the function is determined numerically. The guar anteed result function is shown to be identical with the game value fu nction. When the initial pursuer positions are fixed in an arbitrary m anner there are four game domains depending on their relative position s. The boundary between the ''three-after-one-in-the-middle'' domain a nd the ''three-after-one'' domain is found numerically, and the remain ing boundaries are interior Nicomedean conchoids, lines and circles. P rograms are written that construct singular manifolds and the value fu nction level lines.