Multiple capture in Pontryagin’s almost periodic example

Abstract

This paper considers Pontryagin’s generalized nonstationary example with several participants under the same dynamic and inertial capabilities of the players, in which the set of admissible control actions is a convex compact set and the terminal sets are convex compact sets. We obtain sufficient conditions for the multiple capture of one evader by a group of pursuers under the assumption that some functions associated with the initial data and game parameters are almost periodic. Each pursuer cannot make a capture more than once before being eliminated from the game. Such a situation may happen when the evader must be “terminated” but contact between the pursuer and the evader does not guarantee termination.