Solvability sets in a pursuit game with two pursuers and one evader

S. S. Kumkov   ; S. Le Menec   ; V. S. Patsko

Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 148-165

Résumé

We consider a differential game with two pursuers and one evader. The dynamics of each object is described by a linear stationary system in general form 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. Misses are counted at fixed times. An algorithm for constructing level sets of the value function (solvability sets of the game problem) is described. For the case of “strong” pursuers we give methods for the construction of optimal strategies. Numerical results are presented. This zero-sum game can be useful for studying the concluding stage of a space pursuit involving two pursuing objects and one evading object.

Détail

Keywords: differential games, linear dynamics, value function, optimal feedback control.

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