Evasion Differential Game of One Evader and Many Slow Pursuers

Gafurjan Ibragimov ()
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Gafurjan Ibragimov: Tashkent State University of Economics

Dynamic Games and Applications, 2024, vol. 14, issue 3, No 6, 665-685

Abstract: Abstract We study a simple motion evasion differential game of m pursuers and one evader. The maximum speed of pursuers is 1, and that of evader is $$\sigma > 1$$ σ > 1 . If for all time the state of the evader doesn’t coincide with the state of any pursuer, then evasion is said to be possible. The evader strives to avoid capture. This problem was studied by F.L. Chernous’ko in 1976. We propose a new evasion strategy, which guarantees evasion from any initial positions of players and enables us to estimate the number of approach times from the above by $$m(m+1)/2$$ m ( m + 1 ) / 2 . Also, it is established that all approach times of each pursuer to the evader may occur only on the time interval associated with the first approach time of the pursuer to the evader.

Keywords: Differential game; Evasion; Control; Strategy; Slow pursuers; Primary: 91A23; Secondary: 49N75 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13235-023-00501-2

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