Abstract
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.
Highlights
Equations with fractional-order derivatives and differences are widely used to describe various processes and phenomena
Most of the research in this field deals with the parameter identification of fractionalorder differential equations using the error in an equation or an output error
In article [34], an algorithm was proposed for the parameter identification of discrete fractional systems based on an augmented system of equations
Summary
Equations with fractional-order derivatives and differences are widely used to describe various processes and phenomena. References [6,7,8] presented an overview of different methods for identifying systems with fractional-order derivatives. The use of total least squares for estimating the parameters of fractional-order differential equations was proposed in [9,10]. A small number of articles are devoted to the parameter identification of fractionalorder systems with errors-in-variables. The problem of estimating the parameters of fractional systems with error in variables can be solved based on generalized total least squares [32]. In article [34], an algorithm was proposed for the parameter identification of discrete fractional systems based on an augmented system of equations. This article proposes a symmetrical augmented system of equations with real coefficients for the parameter identification of discrete fractional systems by generalized total least squares. The proposed symmetrical augmented system of equations has a smaller dimension than the augmented system [39], as well as real coefficients
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