On the choice of inputs in identification for robust control
type: Item
instance of: scholarly article
title: On the choice of inputs in identification for robust control
zbMATH Open document ID: 0951.93022
DOI: 10.1016/S0005-1098(99)00002-3
author: Brian D. O. Anderson
author: A. C. Antoulas
published in: Automatica
publication date: 2001-01-03T00:00:00Z
review text: The authors deal with identification in the sense of estimating the coefficients of the numerator and denominator polynomials of a rational transfer function when noisy measurements of both the input and output of the system with this transfer function are known. They begin with the review of the classical approach to design optimal inputs for identification. They also study the identification problem for robust control on the assumption that an upper bound on the norm of the perturbation affecting the data is a priori known. Thus, the second-smallest eigenvalue of an appropriate defined data covariance matrix is a quantity which provides an upper bound for the size of the uncertainty affecting the data. Further it is shown that the problem of computing optimal inputs, reformulated in the frequency domain, is equivalent to a linear matrix inequality problem. For a linear, time-invariant, discrete-time system, an optimal input is designed which maximizes the second-smallest singular value of the data matrix defined in a certain way. Also, the stationary points of the eigenvalues of a certain data covariance matrix \(\mathcal D\) are computed explicitly in terms of the coefficients of the numerator and denominator of the transfer function; this leads to upper and lower bounds of the second-smallest singular value \(\sigma_*\) of \(\mathcal D\). Finally, the results of a simulation experiment are presented comparing the random input with the input obtained by the above-mentioned optimization and the inverse optimal-input problem is discussed.
Mathematics Subject Classification ID: 93B30
Mathematics Subject Classification ID: 15A39
Mathematics Subject Classification ID: 93B35
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 1331907
zbMATH Keywords: robust control
zbMATH Keywords: norm-bounded uncertainty
zbMATH Keywords: convex optimization
zbMATH Keywords: linear matrix inequalities
zbMATH Keywords: identification
reviewed by: Marian Ivanovici
MaRDI profile type: Publication
Wikidata QID: Q127412346
full work available at URL: s0005-1098(99)00002-3
OpenAlex ID: W2027393157
description: scientific article; zbMATH DE number 1331907