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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]
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Database: Engineering Source
Description
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]
ISSN:01423312
DOI:10.1177/01423312251319586