Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares
This paper is devoted to the identification of the parameters of discrete fractional systems with errors in variables. Estimates of the parameters of such systems can be obtained using generalized total least squares (GTLS). A GTLS problem can be reduced to a total least squares (TLS) problem. A tot...
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MDPI AG
2021-12-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/24/3250 |
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| author | Dmitriy Ivanov Aleksandr Zhdanov |
| author_facet | Dmitriy Ivanov Aleksandr Zhdanov |
| author_sort | Dmitriy Ivanov |
| collection | DOAJ |
| description | This paper is devoted to the identification of the parameters of discrete fractional systems with errors in variables. Estimates of the parameters of such systems can be obtained using generalized total least squares (GTLS). A GTLS problem can be reduced to a total least squares (TLS) problem. A total least squares problem is often ill-conditioned. To solve a TLS problem, a classical algorithm based on finding the right singular vector or an algorithm based on an augmented system of equations with complex coefficients can be applied. In this paper, a new augmented system of equations with real coefficients is proposed to solve TLS problems. A symmetrical augmented system of equations was applied to the parameter identification of discrete fractional systems. The simulation results showed that the use of the proposed symmetrical augmented system of equations can shorten the time for solving such problems. It was also shown that the proposed system can have a smaller condition number. |
| first_indexed | 2024-03-10T03:37:29Z |
| format | Article |
| id | doaj.art-b82dd2590e90488b86e9bbcda9f21e51 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T03:37:29Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj.art-b82dd2590e90488b86e9bbcda9f21e512023-11-23T09:26:29ZengMDPI AGMathematics2227-73902021-12-01924325010.3390/math9243250Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least SquaresDmitriy Ivanov0Aleksandr Zhdanov1Department of Information Systems Security, Samara National Research University, 443086 Samara, RussiaDepartment of Applied Mathematics and Computer Science, Samara State Technical University, 443100 Samara, RussiaThis paper is devoted to the identification of the parameters of discrete fractional systems with errors in variables. Estimates of the parameters of such systems can be obtained using generalized total least squares (GTLS). A GTLS problem can be reduced to a total least squares (TLS) problem. A total least squares problem is often ill-conditioned. To solve a TLS problem, a classical algorithm based on finding the right singular vector or an algorithm based on an augmented system of equations with complex coefficients can be applied. In this paper, a new augmented system of equations with real coefficients is proposed to solve TLS problems. A symmetrical augmented system of equations was applied to the parameter identification of discrete fractional systems. The simulation results showed that the use of the proposed symmetrical augmented system of equations can shorten the time for solving such problems. It was also shown that the proposed system can have a smaller condition number.https://www.mdpi.com/2227-7390/9/24/3250fractional differencegeneralized total least squareserrors-in-variablesaugmented system of equationsill conditioning |
| spellingShingle | Dmitriy Ivanov Aleksandr Zhdanov Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares Mathematics fractional difference generalized total least squares errors-in-variables augmented system of equations ill conditioning |
| title | Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares |
| title_full | Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares |
| title_fullStr | Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares |
| title_full_unstemmed | Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares |
| title_short | Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares |
| title_sort | symmetrical augmented system of equations for the parameter identification of discrete fractional systems by generalized total least squares |
| topic | fractional difference generalized total least squares errors-in-variables augmented system of equations ill conditioning |
| url | https://www.mdpi.com/2227-7390/9/24/3250 |
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