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Capture of Given Number of Evaders in Pontryagin’s Nonstationary Example

  • Nikolai N. Petrov
  • Nadezhda A. Solov’evaEmail author
Article
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Abstract

The article deals with Pontryagin’s generalized nonstationary example with n pursuers and m evaders with the same dynamic and inertial capabilities of players. The set of values of admissible controls V is a strictly convex compact set with a smooth boundary. The pursuers use quasi-strategies. Sufficient conditions for the pursuers’ group to capture one evader and the given number of evaders are presented in the terms of the initial position and the parameters of the game. In the problem of catching a given number of evaders, it is assumed that at first all evaders choose their open-loop controls and then the pursuers determine their motions on the basis of the information about the choice of the evaders and, moreover, each pursuer catches no more than one evader.

Keywords

Differential game Group pursuit The objective of capturing Pontryagin’s example Recurrent function 

Notes

Acknowledgements

This work was supported by Grant 1.5211.2017/8.9 by the Ministry of Education and Science of the Russian Federation within the framework of the basic part of the state project in the field of science and Grant 16-01-00346 from Russian Foundation for Basic Research. We sincerely appreciate the efforts of the reviewers of this article. Indeed, their valuable observations, comments and suggestions improve the quality of the work.

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Udmurt State UniversityIzhevskRussia

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