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Stochastic linear quadratic optimal control problem with terminal state constraints.

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Title: Stochastic linear quadratic optimal control problem with terminal state constraints.
Authors: Wang, Hongxia1 (AUTHOR) whx1123@126.com, Hu, Yuxi1 (AUTHOR), Liu, Yihang1 (AUTHOR), Xu, Zhihao1 (AUTHOR), Song, Lianfeng1 (AUTHOR)
Source: Asian Journal of Control. May2024, Vol. 26 Issue 3, p1564-1573. 10p.
Subjects: Stochastic difference equations, Lagrange multiplier, Distribution (Probability theory), Optimal control theory, Boundary value problems, Stochastic systems
Abstract: This paper addresses the stochastic linear quadratic (LQ) control problem with first‐ and second‐order moment constraints on the terminal state. The problem is a modified version of the optimal covariance control problem, where the terminal state is steered to a given probability distribution. Studying a multiplicative‐noise stochastic system rather than an additive‐noise system is a salient feature. Unlike the existing ideas in the optimal steering, by using the Lagrange multipliers method and establishing the stochastic maximum principle, our problem is converted into solving forward–backward stochastic difference equations (FBSDEs), which is a special stochastic two‐point boundary‐value problem (TPBVP). We provide the optimal closed‐loop controller and necessary and sufficient solvability conditions by developing a nonhomogeneous relationship between the optimal state and costate in FBSDEs. Finally, numerical examples are given to demonstrate our results. [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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  Data: Stochastic linear quadratic optimal control problem with terminal state constraints.
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  Data: <searchLink fieldCode="AR" term="%22Wang%2C+Hongxia%22">Wang, Hongxia</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> whx1123@126.com</i><br /><searchLink fieldCode="AR" term="%22Hu%2C+Yuxi%22">Hu, Yuxi</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Liu%2C+Yihang%22">Liu, Yihang</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Xu%2C+Zhihao%22">Xu, Zhihao</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Song%2C+Lianfeng%22">Song, Lianfeng</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. May2024, Vol. 26 Issue 3, p1564-1573. 10p.
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  Data: <searchLink fieldCode="DE" term="%22Stochastic+difference+equations%22">Stochastic difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Lagrange+multiplier%22">Lagrange multiplier</searchLink><br /><searchLink fieldCode="DE" term="%22Distribution+%28Probability+theory%29%22">Distribution (Probability theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Optimal+control+theory%22">Optimal control theory</searchLink><br /><searchLink fieldCode="DE" term="%22Boundary+value+problems%22">Boundary value problems</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+systems%22">Stochastic systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper addresses the stochastic linear quadratic (LQ) control problem with first‐ and second‐order moment constraints on the terminal state. The problem is a modified version of the optimal covariance control problem, where the terminal state is steered to a given probability distribution. Studying a multiplicative‐noise stochastic system rather than an additive‐noise system is a salient feature. Unlike the existing ideas in the optimal steering, by using the Lagrange multipliers method and establishing the stochastic maximum principle, our problem is converted into solving forward–backward stochastic difference equations (FBSDEs), which is a special stochastic two‐point boundary‐value problem (TPBVP). We provide the optimal closed‐loop controller and necessary and sufficient solvability conditions by developing a nonhomogeneous relationship between the optimal state and costate in FBSDEs. Finally, numerical examples are given to demonstrate our results. [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.3285
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 10
        StartPage: 1564
    Subjects:
      – SubjectFull: Stochastic difference equations
        Type: general
      – SubjectFull: Lagrange multiplier
        Type: general
      – SubjectFull: Distribution (Probability theory)
        Type: general
      – SubjectFull: Optimal control theory
        Type: general
      – SubjectFull: Boundary value problems
        Type: general
      – SubjectFull: Stochastic systems
        Type: general
    Titles:
      – TitleFull: Stochastic linear quadratic optimal control problem with terminal state constraints.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Wang, Hongxia
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          Name:
            NameFull: Hu, Yuxi
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            NameFull: Liu, Yihang
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            NameFull: Xu, Zhihao
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          Name:
            NameFull: Song, Lianfeng
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          Dates:
            – D: 01
              M: 05
              Text: May2024
              Type: published
              Y: 2024
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              Value: 26
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            – TitleFull: Asian Journal of Control
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