On the Expansion of a Class of Open-Loop Evasion Control in the Simplest Two-Criteria Pursuit-Evasion Game of Two Purposes

Abstract

The article is devoted to the formulation and solution of the two-criterion pursuit-evasion game on the plane of one pursuer against two targets, one of which is false. A false target is used to distract the pursuer, allowing the true target (in the process of diverting) to maximize the minimum possible distance to the pursuer. The specificity of the pursuer is that it has a circular classification zone of radius R, within which it has the ability to instantly classify the target as false or true. The game is that the pursuer minimizes the time required to approach one of the targets to a distance not exceeding R (R-encounter), and the targets, acting in concert, maximize the minimum distance between the pursuer and the remaining target. The game continues until the R-meeting of the pursuer with the first (false) target, i.e. until the classification of the false target. It is assumed that the first target is false a priori the persecutor is not known. The strategy of using a false target is precisely to release it to distract the pursuer from the true target. In reality, the false target is a mobile drone, which is controlled programmatically by the on-Board computer. In the class of open-loop controls the staging was investigated in 1984 by Ivanov M. N. and Maslov E. P. There is a natural question: what will give an extension of a class of open-loop controls of the false targets to the class of closed-loop controls, i.e. to the class of controls with a feedback? This question is quite appropriate in connection with the great progress in the development of microprocessor technology and improving the performance of on-Board computers, which makes it possible to use more complex algorithms for controlling Autonomous mobile objects. This article gives a negative answer to the above question, namely, it is shown that the extension of the class of open-loop controls by a false target does not improve the quality of control. It is proved that in this game there is a Nash equilibrium in the program strategies of the players.