Linear evasion differential game of one evader and several pursuers with integral constraints

• DOI: 10.1007/s00182-021-00760-6
• Publication Date: 2021-02-11T17:03:49Z
• Authors: Gafurjan Ibragimov; Massimiliano Ferrara; Marks Ruziboev; Bruno Antonio Pan...
• Keywords: Statistics and Probability; Economics and Econometrics; 0209 industrial biotechnology; Mathematics (miscellaneous); 02 engineering and technology; Statistics, Probability and Uncertainty; Energy Research; 101017 Game theory; 101017 Spieltheorie; Social Sciences (miscellaneous)

Abstract An evasion differential game of one evader and many pursuers is studied. The dynamics state variables $$x_1,\ldots , x_m$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>x</mml:mi> <mml:mn>1</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mo>…</mml:mo> <mml:mi>m</mml:mi> </mml:mrow> </mml:math> are described by linear equations. control functions players subjected to integral constraints. If $$x_i(t) \ne 0$$ <mml:mi>i</mml:mi> <mml:mo>(</mml:mo> <mml:mi>t</mml:mi> <mml:mo>)</mml:mo> <mml:mo>≠</mml:mo> <mml:mn>0</mml:mn> for all $$i \in \{1,\ldots ,m\}$$ <mml:mo>∈</mml:mo> <mml:mo>{</mml:mo> <mml:mo>}</mml:mo> $$t \ge <mml:mo>≥</mml:mo> then we say that possible. It assumed the total energy doesn’t exceed evader. We construct an strategy prove any positive integer m