Parametric and nonparametric curve fitting

被引：30

作者：

Hsu, Kenneth ^{[1
]}

Novara, Carlo

Vincent, Tyrone

Milanese, Mario

Poolla, Kameshwar

机构：

[1] Univ Calif Berkeley, Dept Mech Engn, Berkeley, CA 94720 USA

[2] Politecn Torino, Dipartimento Automat & Informat, I-10129 Turin, Italy

[3] Colorado Sch Mines, Div Engn, Golden, CO 80401 USA

来源：

AUTOMATICA | 2006年 / 42卷 / 11期

基金：

美国国家科学基金会;

关键词：

curve fitting; static nonlinearity; persistence of excitation; identifiability; convergence;

D O I：

10.1016/j.automatica.2006.05.024

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We are concerned with convergence issues in the identification of a static nonlinear function. Our investigation focuses on properties of the input signal that ensure convergence of the estimate. Both parametric and nonparametric approaches are considered. In the parametric case, we offer sufficient conditions under which the estimated parameters converge to their true values almost surely. For the nonparametric case, we offer necessary and sufficient conditions under which the estimated function converges almost surely to the true nonlinearity. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：1869 / 1873

页数：5

共 20 条

[1] STRONG CONSISTENCY OF LEAST-SQUARES ESTIMATES IN DYNAMIC-MODELS
ANDERSON, TW
TAYLOR, JB
[J]. ANNALS OF STATISTICS, 1979, 7 (03) : 484 - 489
[2] STRONG CONSISTENCY OF LEAST-SQUARES ESTIMATES IN NORMAL LINEAR-REGRESSION
ANDERSON, TW
TAYLOR, JB
[J]. ANNALS OF STATISTICS, 1976, 4 (04) : 788 - 790
[3] ASTROM KJ, 1985, TFRT3178 LUND I TECH
[4] Some results on optimal experiment design
Forssell, U
Ljung, L
[J]. AUTOMATICA, 2000, 36 (05) : 749 - 756
[5] Identification of non-linear systems using empirical data and prior knowledge - An optimization approach
Johansen, TA
[J]. AUTOMATICA, 1996, 32 (03) : 337 - 356
[6] Nonlinear black-box models in system identification: Mathematical foundations
Juditsky, A
Hjalmarsson, H
Benveniste, A
Delyon, B
Ljung, L
Sjoberg, J
Zhang, QH
[J]. AUTOMATICA, 1995, 31 (12) : 1725 - 1750
[7] KACEWICZ B, 1992, P 1992 C DEC CONTR
[8] Kolmogoroff A, 1930, CR HEBD ACAD SCI, V191, P910
[9] STRONG CONSISTENCY OF LEAST-SQUARES ESTIMATES IN MULTIPLE-REGRESSION
LAI, TL
ROBBINS, H
WEI, CZ
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 1978, 75 (07) : 3034 - 3036
[10] Lancaster P., 1986, CURVE SURFACE FITTIN, V1st ed.

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