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Optimal control problems subject to forward and backward stochastic difference equations.

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Title: Optimal control problems subject to forward and backward stochastic difference equations.
Authors: Chen, Xin1 (AUTHOR) xchen@njust.edu.cn, Yuan, Yue1 (AUTHOR), Yuan, Dongmei2 (AUTHOR)
Source: Asian Journal of Control. Sep2025, Vol. 27 Issue 5, p2488-2502. 15p.
Subjects: Optimal control theory, Stochastic difference equations, Analytical solutions, Quantitative research, Feedback control systems
Abstract: Backward and forward stochastic difference equations are two distinct types of difference equations. In this paper, we explore optimal control problems based on both forward and backward stochastic difference equations. Initially, we study optimal control problems grounded in backward stochastic difference equations and present backward recursive equations as a means of resolving such problems. Through solving these equations, we delve into a bang‐bang optimal control problem, offering an analytical expression for its optimal solution. Building upon these findings, we extend our investigation to encompass a linear quadratic optimal control problem, involving both forward and backward stochastic difference equations. Leveraging backward recursive equations, we derive an analytical expression for the optimal solution to the linear quadratic optimal control problem. Finally, we substantiate the validity of our conclusions through a numerical example. [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
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  Data: Optimal control problems subject to forward and backward stochastic difference equations.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Chen%2C+Xin%22">Chen, Xin</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> xchen@njust.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Yuan%2C+Yue%22">Yuan, Yue</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Yuan%2C+Dongmei%22">Yuan, Dongmei</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Asian+Journal+of+Control%22">Asian Journal of Control</searchLink>. Sep2025, Vol. 27 Issue 5, p2488-2502. 15p.
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  Data: <searchLink fieldCode="DE" term="%22Optimal+control+theory%22">Optimal control theory</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+difference+equations%22">Stochastic difference equations</searchLink><br /><searchLink fieldCode="DE" term="%22Analytical+solutions%22">Analytical solutions</searchLink><br /><searchLink fieldCode="DE" term="%22Quantitative+research%22">Quantitative research</searchLink><br /><searchLink fieldCode="DE" term="%22Feedback+control+systems%22">Feedback control systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Backward and forward stochastic difference equations are two distinct types of difference equations. In this paper, we explore optimal control problems based on both forward and backward stochastic difference equations. Initially, we study optimal control problems grounded in backward stochastic difference equations and present backward recursive equations as a means of resolving such problems. Through solving these equations, we delve into a bang‐bang optimal control problem, offering an analytical expression for its optimal solution. Building upon these findings, we extend our investigation to encompass a linear quadratic optimal control problem, involving both forward and backward stochastic difference equations. Leveraging backward recursive equations, we derive an analytical expression for the optimal solution to the linear quadratic optimal control problem. Finally, we substantiate the validity of our conclusions through a numerical example. [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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      – Type: doi
        Value: 10.1002/asjc.3592
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 15
        StartPage: 2488
    Subjects:
      – SubjectFull: Optimal control theory
        Type: general
      – SubjectFull: Stochastic difference equations
        Type: general
      – SubjectFull: Analytical solutions
        Type: general
      – SubjectFull: Quantitative research
        Type: general
      – SubjectFull: Feedback control systems
        Type: general
    Titles:
      – TitleFull: Optimal control problems subject to forward and backward stochastic difference equations.
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            NameFull: Chen, Xin
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            NameFull: Yuan, Yue
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            NameFull: Yuan, Dongmei
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            – D: 01
              M: 09
              Text: Sep2025
              Type: published
              Y: 2025
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              Value: 27
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              Value: 5
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            – TitleFull: Asian Journal of Control
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