Solvability sets in pursuit problem with two pursuers and one evader

Abstract

The paper deals with a differential game with two pursuers and one evader. Dynamics of each object is described by a stationary linear system of a general type with a scalar control. The payoff is the minimum of two one-dimensional misses between the first pursuer and the evader and between the second pursuer and the evader. The misses are calculated at the instants fixed in advance. A method is described for constructing the level sets of the value function (i.e., the solvability ones for the game under consideration). For the case of "strong" pursuers, the optimal strategies are described. Results of simulations are given. The zero-sum game investigated can be useful for the research of the final stage of a space pursuit, where two pursuing objects and one evader are involved. © IFAC.