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Distributed Nash equilibrium seeking for uncertain linear multi‐agent systems by output feedback integral control.

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Title: Distributed Nash equilibrium seeking for uncertain linear multi‐agent systems by output feedback integral control.
Authors: Zheng, Xianxian1 (AUTHOR), Wei, Lan2 (AUTHOR), Yi, Peng3,4,5,6 (AUTHOR), Tang, Yutao1 (AUTHOR) yttang@bupt.edu.cn
Source: Asian Journal of Control. May2026, Vol. 28 Issue 3, p1318-1325. 8p.
Subjects: Nash equilibrium, Multiagent systems, Nash, John F., 1928-2015, Control theory (Engineering), Noncooperative games (Mathematics), Linear dynamical systems, Observability (Control theory), Feedback control systems
Abstract: This paper is focused on the Nash equilibrium seeking problem for a group of high‐order dynamic players. Each player possesses a general linear dynamic with parameter uncertainties. To solve this problem, we first introduce a virtual reference generator for each player by virtue of the embedded design approach and then constructively propose an observer‐based output feedback integral controller relying on local information and computation. The decision outputs of all players are rigorously proven to reach the expected Nash equilibrium of the corresponding noncooperative game irrespective of the model uncertainties. We also give a simulation example to illustrate the effectiveness of our algorithms. [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.)
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  Label: Title
  Group: Ti
  Data: Distributed Nash equilibrium seeking for uncertain linear multi‐agent systems by output feedback integral control.
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  Data: <searchLink fieldCode="AR" term="%22Zheng%2C+Xianxian%22">Zheng, Xianxian</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wei%2C+Lan%22">Wei, Lan</searchLink><relatesTo>2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yi%2C+Peng%22">Yi, Peng</searchLink><relatesTo>3,4,5,6</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Tang%2C+Yutao%22">Tang, Yutao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> yttang@bupt.edu.cn</i>
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  Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. May2026, Vol. 28 Issue 3, p1318-1325. 8p.
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  Data: <searchLink fieldCode="DE" term="%22Nash+equilibrium%22">Nash equilibrium</searchLink><br /><searchLink fieldCode="DE" term="%22Multiagent+systems%22">Multiagent systems</searchLink><br /><searchLink fieldCode="DE" term="%22Nash%2C+John+F%2E%2C+1928-2015%22">Nash, John F., 1928-2015</searchLink><br /><searchLink fieldCode="DE" term="%22Control+theory+%28Engineering%29%22">Control theory (Engineering)</searchLink><br /><searchLink fieldCode="DE" term="%22Noncooperative+games+%28Mathematics%29%22">Noncooperative games (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Linear+dynamical+systems%22">Linear dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Observability+%28Control+theory%29%22">Observability (Control theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: This paper is focused on the Nash equilibrium seeking problem for a group of high‐order dynamic players. Each player possesses a general linear dynamic with parameter uncertainties. To solve this problem, we first introduce a virtual reference generator for each player by virtue of the embedded design approach and then constructively propose an observer‐based output feedback integral controller relying on local information and computation. The decision outputs of all players are rigorously proven to reach the expected Nash equilibrium of the corresponding noncooperative game irrespective of the model uncertainties. We also give a simulation example to illustrate the effectiveness of our algorithms. [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.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1002/asjc.3739
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 8
        StartPage: 1318
    Subjects:
      – SubjectFull: Nash equilibrium
        Type: general
      – SubjectFull: Multiagent systems
        Type: general
      – SubjectFull: Nash, John F., 1928-2015
        Type: general
      – SubjectFull: Control theory (Engineering)
        Type: general
      – SubjectFull: Noncooperative games (Mathematics)
        Type: general
      – SubjectFull: Linear dynamical systems
        Type: general
      – SubjectFull: Observability (Control theory)
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
    Titles:
      – TitleFull: Distributed Nash equilibrium seeking for uncertain linear multi‐agent systems by output feedback integral control.
        Type: main
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          Name:
            NameFull: Zheng, Xianxian
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            NameFull: Wei, Lan
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            NameFull: Yi, Peng
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            NameFull: Tang, Yutao
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          Dates:
            – D: 01
              M: 05
              Text: May2026
              Type: published
              Y: 2026
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              Value: 28
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            – TitleFull: Asian Journal of Control
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