Nonlinear differential game “pursuit-evasion”: information aspect.

Abstract

The article deals with the information aspects of the nonlinear differential game “pursuit-evasion”. The mini- max quality criterion (the price of the game), mathematical models of the movement of the same type of players are set. The main problem that arises in the practical consideration of a nonlinear differential game is the solution of a boundary value problem. It is proved that: 1) a differential game can be represented as an envelope of a family of singular curves (“instantaneous solutions”) constructed from each of its points, 2) the control of the players can be found on this family. The method of constructing instant solutions is justified. The principle of information dualism in the differential game “pursuit-evasion” is proved. Its use facilitates the solution of information and computational problems that arise during the implementation of the game.