Symmetrical Augmented System of Equations for the Parameter Identification of Discrete Fractional Systems by Generalized Total Least Squares

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.

Model Identification and Control of Electromagnetic Actuation in Continuous Casting Process With Improved Quality

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Implicit iterative algorithm for solving regularized total least squares problems

“…The classical algorithm for solving the total least squares problem based on SVD (singular value decomposition) [12]. The solution of the total least squares problem based on augmented systems is considered in [13,14]. To solve large-scale linear systems of equations or linear systems of equations with a sparse matrix, iterative algorithms for total least squares are used: the Newton method [15,16], Rayleigh iterations [17], Lanchotz iterations [18].…”