A decomposition technique for pursuit evasion games with many pursuers

Memory storage constraints impose ultimate limits on the complexity of differential games for which optimal strategies can be computed via direct solution of the associated Hamilton-Jacobi-Isaacs equations. It is of interest therefore to explore whether, for certain specially structured differential games of interest, it is possible to decompose the original problem into a family of simpler differential games. In this paper we exhibit a class of single evader-multiple pursuers games for which a reduction in complexity of this nature is possible. The target set is expressed as a union of smaller, sub-target sets. The individual differential games are obtained by substituting a sub-target set in place of the original target and are simpler because of geometric features of the dynamics and constraints. We give conditions under which the value function of the original problem can be characterized as the lower envelope of the value functions for the simpler problems and show how optimal strategies can be constructed from those for the simpler problems. The methodology is illustrated by several examples.