Abstract
We consider a generalized non-stationary Pontryagin's example under the same dynamic and inertial capabilities players and phase constraints on the state of the runaway. Boundary of phase constraints is not a line of death for the evader. Sufficient conditions for the capture of a group of pursuers one evader are obtained in this article.
Highlights
Differential games of two players, first considered in the book of Isaacs [1], present wide field of research [2]-[8]
Methods were developed for solving various classes of game problems: Isaaks’ method, based on the analysis of a certain partial differential equation and its characteristics; Krasovskii’s method of extremal guidans; Pontryagin’s method and others
Solov’eva pursuers and one or several evaders [9]-[12]. These games are interesting from the theoretical point of view, they cannot be solved by theory for two-person games
Summary
Differential games of two players, first considered in the book of Isaacs [1], present wide field of research [2]-[8]. Solov’eva pursuers and one or several evaders [9]-[12] These games are interesting from the theoretical point of view, they cannot be solved by theory for two-person games. One reason for this is, that the union sets of the reachability of all pursuers and the union of all target sets are sets, is non-convex and, is not connected. There are some applications of these games to the problems of motion vehicles, collisions of avoidance for ships and others In this case, the problem becomes much more complicated if the players on the state of the phase constraints are imposed. In this paper we consider the problem of persecution of a group of pursuers one evader at equal opportunities and inertial dynamic players. Provided that some of the functions defined by the initial conditions and parameters of the game are recurrent, we obtain sufficient conditions for the solvability of persecution
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