Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub>
The present paper is devoted to studying a pursuit differential game described by an infinite system of binary differential equations in Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi...
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| Format: | Article |
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MDPI AG
2023-06-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/12/2662 |
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| author | Gafurjan Ibragimov Xolmurodjon Qushaqov Akbarjon Muxammadjonov Bruno Antonio Pansera |
| author_facet | Gafurjan Ibragimov Xolmurodjon Qushaqov Akbarjon Muxammadjonov Bruno Antonio Pansera |
| author_sort | Gafurjan Ibragimov |
| collection | DOAJ |
| description | The present paper is devoted to studying a pursuit differential game described by an infinite system of binary differential equations in Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>2</mn></msub></semantics></math></inline-formula>. The control parameters of the players are subject to geometric constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>2</mn></msub></semantics></math></inline-formula>, and oppositely, the evader tries to avoid it. Our aim is to construct a strategy for the pursuer to complete a differential game and an evasion control. We obtain an equation for the guaranteed pursuit and evasion times. |
| first_indexed | 2024-03-11T02:12:06Z |
| format | Article |
| id | doaj.art-18102c783dde44129ed2e0858d7935fe |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-11T02:12:06Z |
| publishDate | 2023-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-18102c783dde44129ed2e0858d7935fe2023-11-18T11:28:03ZengMDPI AGMathematics2227-73902023-06-011112266210.3390/math11122662Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub>Gafurjan Ibragimov0Xolmurodjon Qushaqov1Akbarjon Muxammadjonov2Bruno Antonio Pansera3Department of General and Exact Subjects, Tashkent State University of Economics, Tashkent 100006, UzbekistanDepartment of Mathematics, Andijan State University, Andijan 170100, UzbekistanDepartment of Mathematics, Andijan State University, Andijan 170100, UzbekistanDepartment of Law, Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria, I-89124 Reggio Calabria, ItalyThe present paper is devoted to studying a pursuit differential game described by an infinite system of binary differential equations in Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>2</mn></msub></semantics></math></inline-formula>. The control parameters of the players are subject to geometric constraints. The pursuer tries to bring the state of the system to the origin of the Hilbert space <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>l</mi><mn>2</mn></msub></semantics></math></inline-formula>, and oppositely, the evader tries to avoid it. Our aim is to construct a strategy for the pursuer to complete a differential game and an evasion control. We obtain an equation for the guaranteed pursuit and evasion times.https://www.mdpi.com/2227-7390/11/12/2662differential gamepursuitcontrolstrategyinfinite system of differential equationsgeometric constraint |
| spellingShingle | Gafurjan Ibragimov Xolmurodjon Qushaqov Akbarjon Muxammadjonov Bruno Antonio Pansera Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub> Mathematics differential game pursuit control strategy infinite system of differential equations geometric constraint |
| title | Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub> |
| title_full | Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub> |
| title_fullStr | Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub> |
| title_full_unstemmed | Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub> |
| title_short | Guaranteed Pursuit and Evasion Times in a Differential Game for an Infinite System in Hilbert Space <i>l</i><sub>2</sub> |
| title_sort | guaranteed pursuit and evasion times in a differential game for an infinite system in hilbert space i l i sub 2 sub |
| topic | differential game pursuit control strategy infinite system of differential equations geometric constraint |
| url | https://www.mdpi.com/2227-7390/11/12/2662 |
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