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H 2 optimal model reduction of positive systems by the augmented Lagrangian method on the oblique manifold.

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Title: H 2 optimal model reduction of positive systems by the augmented Lagrangian method on the oblique manifold.
Authors: Yang, Ping1,2 (AUTHOR), Wang, Zhao-Hong1 (AUTHOR) zhwang@xju.edu.cn, Jiang, Yao-Lin2 (AUTHOR)
Source: Transactions of the Institute of Measurement & Control. Jun2026, Vol. 48 Issue 9, p1667-1677. 11p.
Subjects: Positive systems, Constrained optimization, Numerical analysis, Manifolds (Mathematics), Conjugate gradient methods, Optimization algorithms
Abstract: This paper focuses on the H 2 optimal model reduction problem of positive systems. According to the coefficient matrices of the positive system, the nonnegative orthonormal matrix is taken as the projection matrix, and the H 2 optimal model reduction problem is developed. Since the projection matrix is orthonormal and nonnegative, the H 2 optimal model reduction problem is reformulated as a constrained optimization problem defined on the Stiefel manifold, and further regarded as a constrained optimization problem defined on the oblique manifold. By the augmented Lagrangian function, the constrained optimization problem defined on the oblique manifold is tackled by employing the Dai-Yuan-type conjugate gradient method to solve a series of unconstrained optimization subproblems. When the objective function of a subproblem satisfies some conditions, the iterative sequence produced by the conjugate gradient method is convergent. Finally, numerical experiments illustrate the efficiency of the proposed model reduction method. [ABSTRACT FROM AUTHOR]
Copyright of Transactions of the Institute of Measurement & Control is the property of Sage Publications, Ltd. 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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DbLabel: Engineering Source
An: 193925922
AccessLevel: 6
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  Label: Title
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  Data: H <subscript>2</subscript> optimal model reduction of positive systems by the augmented Lagrangian method on the oblique manifold.
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  Data: <searchLink fieldCode="AR" term="%22Yang%2C+Ping%22">Yang, Ping</searchLink><relatesTo>1,2</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Wang%2C+Zhao-Hong%22">Wang, Zhao-Hong</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> zhwang@xju.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Jiang%2C+Yao-Lin%22">Jiang, Yao-Lin</searchLink><relatesTo>2</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Transactions+of+the+Institute+of+Measurement+%26+Control%22">Transactions of the Institute of Measurement & Control</searchLink>. Jun2026, Vol. 48 Issue 9, p1667-1677. 11p.
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  Data: <searchLink fieldCode="DE" term="%22Positive+systems%22">Positive systems</searchLink><br /><searchLink fieldCode="DE" term="%22Constrained+optimization%22">Constrained optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Numerical+analysis%22">Numerical analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Manifolds+%28Mathematics%29%22">Manifolds (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Conjugate+gradient+methods%22">Conjugate gradient methods</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This paper focuses on the H 2 optimal model reduction problem of positive systems. According to the coefficient matrices of the positive system, the nonnegative orthonormal matrix is taken as the projection matrix, and the H 2 optimal model reduction problem is developed. Since the projection matrix is orthonormal and nonnegative, the H 2 optimal model reduction problem is reformulated as a constrained optimization problem defined on the Stiefel manifold, and further regarded as a constrained optimization problem defined on the oblique manifold. By the augmented Lagrangian function, the constrained optimization problem defined on the oblique manifold is tackled by employing the Dai-Yuan-type conjugate gradient method to solve a series of unconstrained optimization subproblems. When the objective function of a subproblem satisfies some conditions, the iterative sequence produced by the conjugate gradient method is convergent. Finally, numerical experiments illustrate the efficiency of the proposed model reduction method. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Transactions of the Institute of Measurement & Control is the property of Sage Publications, Ltd. 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: 10.1177/01423312251319586
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      – Code: eng
        Text: English
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      Pagination:
        PageCount: 11
        StartPage: 1667
    Subjects:
      – SubjectFull: Positive systems
        Type: general
      – SubjectFull: Constrained optimization
        Type: general
      – SubjectFull: Numerical analysis
        Type: general
      – SubjectFull: Manifolds (Mathematics)
        Type: general
      – SubjectFull: Conjugate gradient methods
        Type: general
      – SubjectFull: Optimization algorithms
        Type: general
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      – TitleFull: H 2 optimal model reduction of positive systems by the augmented Lagrangian method on the oblique manifold.
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            NameFull: Yang, Ping
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            NameFull: Wang, Zhao-Hong
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            NameFull: Jiang, Yao-Lin
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            – D: 01
              M: 06
              Text: Jun2026
              Type: published
              Y: 2026
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              Value: 48
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            – TitleFull: Transactions of the Institute of Measurement & Control
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