Feasible solution to discrete‐time linear quadratic stochastic Stackelberg difference game.
Saved in:
| Title: | Feasible solution to discrete‐time linear quadratic stochastic Stackelberg difference game. |
|---|---|
| Authors: | Qi, Qingyuan1 (AUTHOR), Zhang, Qianqian2 (AUTHOR), Sun, Yue1 (AUTHOR) syue@hrbeu.edu.cn |
| Source: | Asian Journal of Control. May2024, Vol. 26 Issue 3, p1442-1458. 17p. |
| Subjects: | Stochastic differential equations, Stochastic difference equations, Riccati equation |
| Abstract: | This paper investigates the discrete‐time linear quadratic (LQ) stochastic Stackelberg game, which has not been thoroughly addressed in previous literature. Firstly, we derive the maximum principle for the stochastic Stackelberg difference game using the variational method, and obtain the necessary and sufficient solvability conditions. However, due to the coupling between the two players and the presence of stochastic noise, obtaining explicit optimal leader and follower's strategies becomes challenging. Therefore, we present a feasible suboptimal control strategy instead. As a result, we derive a feasible suboptimal control strategy. To achieve this, we assume a linear homogeneous relationship to decouple the group of stochastic game forward‐backward stochastic differential equations (SG‐FBSDEs), which serves as a compromise for obtaining the optimal solution. With this approach, we derive a feasible solution to the stochastic Stackelberg difference game based on the solution to symmetric Riccati equations. [ABSTRACT FROM AUTHOR] |
| Copyright of Asian Journal of Control is the property of Wiley-Blackwell 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 |
|
Full text is not displayed to guests.
Login for full access.
|
|
| FullText | Links: – Type: pdflink Text: Availability: 1 |
|---|---|
| Header | DbId: egs DbLabel: Engineering Source An: 176988020 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: Feasible solution to discrete‐time linear quadratic stochastic Stackelberg difference game. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Qi%2C+Qingyuan%22">Qi, Qingyuan</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Zhang%2C+Qianqian%22">Zhang, Qianqian</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Sun%2C+Yue%22">Sun, Yue</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> syue@hrbeu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. May2024, Vol. 26 Issue 3, p1442-1458. 17p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Stochastic+differential+equations%22">Stochastic differential equations</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+difference+equations%22">Stochastic difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Riccati+equation%22">Riccati equation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper investigates the discrete‐time linear quadratic (LQ) stochastic Stackelberg game, which has not been thoroughly addressed in previous literature. Firstly, we derive the maximum principle for the stochastic Stackelberg difference game using the variational method, and obtain the necessary and sufficient solvability conditions. However, due to the coupling between the two players and the presence of stochastic noise, obtaining explicit optimal leader and follower's strategies becomes challenging. Therefore, we present a feasible suboptimal control strategy instead. As a result, we derive a feasible suboptimal control strategy. To achieve this, we assume a linear homogeneous relationship to decouple the group of stochastic game forward‐backward stochastic differential equations (SG‐FBSDEs), which serves as a compromise for obtaining the optimal solution. With this approach, we derive a feasible solution to the stochastic Stackelberg difference game based on the solution to symmetric Riccati equations. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Asian Journal of Control is the property of Wiley-Blackwell 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=176988020 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1002/asjc.3266 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 17 StartPage: 1442 Subjects: – SubjectFull: Stochastic differential equations Type: general – SubjectFull: Stochastic difference equations Type: general – SubjectFull: Riccati equation Type: general Titles: – TitleFull: Feasible solution to discrete‐time linear quadratic stochastic Stackelberg difference game. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Qi, Qingyuan – PersonEntity: Name: NameFull: Zhang, Qianqian – PersonEntity: Name: NameFull: Sun, Yue IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 05 Text: May2024 Type: published Y: 2024 Identifiers: – Type: issn-print Value: 15618625 Numbering: – Type: volume Value: 26 – Type: issue Value: 3 Titles: – TitleFull: Asian Journal of Control Type: main |
| ResultId | 1 |
