Hüseyin Akçay

Orthonormal basis functions for modelling continuous-time systems

This paper studies continuous-time system model sets that are spanned by xed pole orthonormal bases. The nature of these bases is such as to generalise the well-known Laguerre and two-parameter Kautz bases. The contribution of the paper is to establish that the obtained model sets are complete in all of the Hardy spaces H p (P), 1(p(R, and the right half plane algebra A(P) provided that a mild condition on the choice of basis poles is satised. A characterisation of how modelling accuracy is a!ected by pole choice, as well as an application example of #exible structure modelling are also provided. ( 1999 Elsevier Science B.V. All rights reserved. Zusammenfassung In diesem Artikel werden Modellmengen fuK r Systeme in stetiger Zeit betrachtet, wobei diese Mengen von orthonormalen Basen mit xierten Polen erzeugt werden. Diese Basen verallgemeinern die wohlbekannten Laguerre-Basen und die zweiparametrigen Kautz-Basen. In dieser Arbeit wird gezeigt, dass die erhaltenen Modellmengen in allen Hardy-RaK umen H p (P), 1(p(R, und in der Algebra A(P) der rechten Halbebene vollstaK ndig sind, vorausgesetzt, dass eine schwache Bedingung an die Pole der Basis erfuK llt ist. Eine Charakterisierung des Ein#usses der Polvorgabe auf die Modellgenauigkeit, sowie ein Anwendungsbeispiel der Modellierung einer #exiblen Struktur werden gegeben. ( 1999 Elsevier Science B.V. All rights reserved. Re2 sume2

Rational Basis Functions for Robust Identification from Frequency and Time-Domain Measurements

This paper investigates the use of general bases with fixed poles for the purposes of robust estimation. These bases, which generalise the common FIR, Laguerre and two-parameter Kautz ones, are shown to be fundamental in the disc algebra provided a very mild condition on the choice of poles is satisfied. It is also shown that, by using a min-max criterion, these bases lead to robust estimators for which error bounds in different norms can be explicitly quantified. The key idea facilitating this analysis is to re-parameterise the chosen model structures into a new one with equivalent fixed poles, but for which the basis functions are orthonormal in H2(D).

Orthonormal Basis Functions for Continuous-Time Systems and Lp Convergence

Abstract. In this paper, model sets for linear-time-invariant continuous-time systems that are spanned by fixed pole orthonormal bases are investigated. These bases generalize the well-known Laguerre and two-parameter Kautz cases. It is shown that the obtained model sets are everywhere dense in the Hardy space H1(Π) under the same condition as previously derived by the authors for the denseness in the (Π is the open right half plane) Hardy spaces Hp(Π), 1<p<∞. As a further extension, the paper shows how orthonormal model sets, that are everywhere dense in Hp(Π), 1≤p<∞, and which have a prescribed asymptotic order, may be constructed. Finally, it is established that the Fourier series formed by orthonormal basis functions converge in all spaces Hp(Π) and (D is the open unit disk) Hp(D), 1<p<∞. The results in this paper have application in system identification, model reduction, and control system synthesis.

The least squares algorithm, parametric system identification and bounded noise

Abstract The least squares parametric system identification algorithm is analyzed assuming that the noise is a bounded signal. A bound on the worst-case parameter estimation error is derived. This bound shows that the worst-case parameter estimation error decreases to zero as the bound on the noise is decreased to zero.

Brief paper: Frequency domain subspace-based identification of discrete-time power spectra from uniformly spaced measurements

In this paper, we present a new subspace based algorithm for the identification of multi-input/multi-output, square, discrete-time, linear-time invariant systems from nonuniformly spaced power spectrum measurements. The algorithm is strongly consistent and it is illustrated with one practical example that solves a stochastic road modeling problem.

Subspace-based identification of power transformer models from frequency response data

A recent frequency-domain, subspace-based algorithm is used in the identification of two power transformers. The results indicate that the subspace-based identification algorithms can be used without modification even when the dynamic range of frequency response data is large.

Identification of power transformer models from frequency response data: a case study

Abstract A recent frequency-domain, subspace-based algorithm as well as the well-known nonlinear least-squares algorithm are used in the identification of a power transformer whose frequency response has a dynamic range of 1xa0MHz. When the model complexity is not restricted, both the algorithms produce highly accurate models. Low-complexity models are extracted from the high-order identified ones via the method of balanced truncation. It is observed that this two-step procedure yields more accurate results than an approach of direct identification of a low-order model. The utility of identified models for the purpose of transformer fault detection is also briefly discussed.

Discrete-time system modelling in Lp with orthonormal basis functions

Abstract In this paper, model sets for linear time-invariant systems spanned by fixed pole orthonormal bases are investigated. The obtained model sets are shown to be complete in L p ( T ) (1 , the Lebesque spaces of functions on the unit circle T , and in C( T ) , the space of periodic continuous functions on T . The L p norm error bounds for estimating systems in L p ( T ) by the partial sums of the Fourier series formed by the orthonormal functions are computed for the case 1 . Some inequalities on the mean growth of the Fourier series are also derived. These results have application in estimation and model reduction.

Subspace based identification of power transformer models from frequency response data

A frequency-domain, subspace-based algorithm is used in the identification of two power transformers. The results indicate that the subspace-based identification algorithms can be used without modification even when the dynamic range of frequency response data is large.

On the worst-case divergence of the least-squares algorithm

We provide an H/spl infin/-norm lower bound on the worst-case identification error of least-squares estimation when using FIR model structures. This bound increases as a logarithmic function of model complexity and is valid for a wide class of inputs characterized as being quasi-stationary with covariance function falling off sufficiently quickly.