Data-dependent orthogonal polynomials on generalized circles: A unified approach applied to [formula omitted]-domain identification

Robbert Voorhoeve,Tom Oomen

doi:10.1016/j.automatica.2021.109709

Abstract

The performance of algorithms in system identification and control, depends on their implementation in finite-precision arithmetic. The aim of this paper is to develop a unified approach for numerically reliable system identification that combines the numerical advantages of data-dependent orthogonal polynomials and the discrete-time δ-domain parametrization. In this paper, earlier results for discrete orthogonal polynomials on the real-line and the unit-circle are generalized to obtain an approach for the construction of orthogonal polynomials on generalized circles in the complex plane. This enables the formulation of a unified framework for the numerically reliable identification of systems expressed in the δ-domain, as well as in the traditional Laplace and Z-domains. An example is presented which shows the significant numerical advantages of the δ-domain approach for the identification of fast-sampled systems.

Highlights

Robust and accurate implementation of algorithms used in system identification and control is essential for their successful application (Datta, 2004; Varga, 2004)
The aim of this paper is to develop a unified approach for numerically reliable system identification that combines the numerical advantages of data-dependent orthogonal polynomials and the discrete-time δ-domain parametrization
The results are presented for the Active Vibration Isolation System (AVIS) example

Summary

Introduction

Robust and accurate implementation of algorithms used in system identification and control is essential for their successful application (Datta, 2004; Varga, 2004). This numerical aspect becomes more relevant and challenging as the system complexity increases (Benner, 2004; Oomen et al, 2014). Several approaches that address the encountered numerical issues have been proposed. The use of the discrete δdomain as opposed to the classical Z -domain addresses several numerical issues in digital control implementations with fast sampling (Goodwin, Middleton, & Poor, 1992). The central computational step typically involves solving a linear least squares problem, which often is severely ill-conditioned

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