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

Nikolai N. Petrov () and Nadezhda A. Solov’eva ()
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Nikolai N. Petrov: Udmurt State University
Nadezhda A. Solov’eva: Udmurt State University

Dynamic Games and Applications, 2019, vol. 9, issue 3, No 4, 614-627

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13235-019-00303-5

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