Non-stationary Differential-Difference Games of Neutral Type

Abstract

We consider the pursuit problem for 2-person conflict-controlled process with single pursuer and single evader. The problem is given by the system of the linear functional-differential equations of neutral type. The players pursue their own goals and choose controls in the form of functions of a certain kind. The goal of the pursuer is to catch the evader in the shortest possible time. The goal of the evader is to avoid the meeting of the players’ trajectories on a whole semiinfinite interval of time or if it is impossible to maximally postpone the moment of meeting. For such a conflict-controlled process, we derive conditions on its parameters and initial state, which are sufficient for the trajectories of the players to meet at a certain moment of time for any counteractions of the evader.

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Correspondence to Ievgen Liubarshchuk.

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Liubarshchuk, I., Bihun, Y. & Cherevko, I. Non-stationary Differential-Difference Games of Neutral Type. Dyn Games Appl 9, 771–779 (2019). https://doi.org/10.1007/s13235-019-00298-z

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Keywords

  • Differential-difference games
  • Dynamic games
  • Pursuit problem
  • The Method of Resolving Functions