Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra.
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| Title: | Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra. |
|---|---|
| Authors: | Kuvshinov, D. R.1,2 kuvshinovdr@yandex.ru, Osipov, S. I.2 Sergei.Osipov@urfu.ru |
| Source: | Automation & Remote Control. Mar2018, Vol. 79 Issue 3, p479-491. 13p. |
| Subjects: | Differential games, Polyhedra models, Optimal control theory, Numerical solutions for linear algebra, Zero sum games |
| Abstract: | We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum positional differential games developed by N.N. Krasovskii and his scientific school. The problem of finding a Stackelberg solution reduces to solving nonstandard optimal control problems. We propose an approach based on operations with convex polyhedra. [ABSTRACT FROM AUTHOR] |
| Copyright of Automation & Remote Control is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kuvshinov%2C+D%2E+R%2E%22">Kuvshinov, D. R.</searchLink><relatesTo>1,2</relatesTo><i> kuvshinovdr@yandex.ru</i><br /><searchLink fieldCode="AR" term="%22Osipov%2C+S%2E+I%2E%22">Osipov, S. I.</searchLink><relatesTo>2</relatesTo><i> Sergei.Osipov@urfu.ru</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Automation+%26+Remote+Control%22">Automation & Remote Control</searchLink>. Mar2018, Vol. 79 Issue 3, p479-491. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Differential+games%22">Differential games</searchLink><br /><searchLink fieldCode="DE" term="%22Polyhedra+models%22">Polyhedra models</searchLink><br /><searchLink fieldCode="DE" term="%22Optimal+control+theory%22">Optimal control theory</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+solutions+for+linear+algebra%22">Numerical solutions for linear algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Zero+sum+games%22">Zero sum games</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We consider the problem of constructing approximate Stackelberg solutions in a linear non-zero-sum positional differential game of two players with terminal payoffs and player controls chosen on convex polyhedra. A formalization of player strategies and motions generated by them is based on the formalization and results of the theory of zero-sum positional differential games developed by N.N. Krasovskii and his scientific school. The problem of finding a Stackelberg solution reduces to solving nonstandard optimal control problems. We propose an approach based on operations with convex polyhedra. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Automation & Remote Control is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1134/S0005117918030074 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 479 Subjects: – SubjectFull: Differential games Type: general – SubjectFull: Polyhedra models Type: general – SubjectFull: Optimal control theory Type: general – SubjectFull: Numerical solutions for linear algebra Type: general – SubjectFull: Zero sum games Type: general Titles: – TitleFull: Numerical Construction of Stackelberg Solutions in a Linear Positional Differential Game Based on the Method of Polyhedra. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kuvshinov, D. R. – PersonEntity: Name: NameFull: Osipov, S. I. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2018 Type: published Y: 2018 Identifiers: – Type: issn-print Value: 00051179 Numbering: – Type: volume Value: 79 – Type: issue Value: 3 Titles: – TitleFull: Automation & Remote Control Type: main |
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