Adaptive hinging hyperplanes and its applications in dynamic system identification

Jun Xu; Xiaolin Huang; Shuning Wang

doi:10.1016/j.automatica.2009.06.013

Adaptive hinging hyperplanes and its applications in dynamic system identification

Jun Xu^*
, Xiaolin Huang
, Shuning Wang

^*Corresponding author for this work

Tsinghua University

Research output: Contribution to journal › Article › peer-review

49 Scopus citations

Abstract

The model of adaptive hinging hyperplanes (AHH) is proposed in this paper. It is based on multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subregion. The AHH model is actually a special case of the GHH model, which has a universal representation capability for continuous piecewise linear functions. The approximation ability of the AHH model is proved. The AHH algorithm is developed similar to the MARS algorithm. It is adaptive and can be executed efficiently, hence has power and flexibility to model unknown relationships. The AHH procedure is applied to identifying two dynamic systems and its potential is illustrated.

Original language	English
Pages (from-to)	2325-2332
Number of pages	8
Journal	Automatica
Volume	45
Issue number	10
DOIs	https://doi.org/10.1016/j.automatica.2009.06.013
State	Published - Oct 2009
Externally published	Yes

Keywords

Adaptive regression
Identification methods
Piecewise-linear
System model validation

Access to Document

10.1016/j.automatica.2009.06.013

Cite this

@article{72e3f66fbc77427487e1b890a288ef41,

title = "Adaptive hinging hyperplanes and its applications in dynamic system identification",

abstract = "The model of adaptive hinging hyperplanes (AHH) is proposed in this paper. It is based on multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subregion. The AHH model is actually a special case of the GHH model, which has a universal representation capability for continuous piecewise linear functions. The approximation ability of the AHH model is proved. The AHH algorithm is developed similar to the MARS algorithm. It is adaptive and can be executed efficiently, hence has power and flexibility to model unknown relationships. The AHH procedure is applied to identifying two dynamic systems and its potential is illustrated.",

keywords = "Adaptive regression, Identification methods, Piecewise-linear, System model validation",

author = "Jun Xu and Xiaolin Huang and Shuning Wang",

year = "2009",

month = oct,

doi = "10.1016/j.automatica.2009.06.013",

language = "英语",

volume = "45",

pages = "2325--2332",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier Ltd",

number = "10",

}

TY - JOUR

T1 - Adaptive hinging hyperplanes and its applications in dynamic system identification

AU - Xu, Jun

AU - Huang, Xiaolin

AU - Wang, Shuning

PY - 2009/10

Y1 - 2009/10

N2 - The model of adaptive hinging hyperplanes (AHH) is proposed in this paper. It is based on multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subregion. The AHH model is actually a special case of the GHH model, which has a universal representation capability for continuous piecewise linear functions. The approximation ability of the AHH model is proved. The AHH algorithm is developed similar to the MARS algorithm. It is adaptive and can be executed efficiently, hence has power and flexibility to model unknown relationships. The AHH procedure is applied to identifying two dynamic systems and its potential is illustrated.

AB - The model of adaptive hinging hyperplanes (AHH) is proposed in this paper. It is based on multivariate adaptive regression splines (MARS) and generalized hinging hyperplanes (GHH) and shares attractive properties of the two. By making a modification to the basis function of MARS, AHH shows linear property in each subregion. The AHH model is actually a special case of the GHH model, which has a universal representation capability for continuous piecewise linear functions. The approximation ability of the AHH model is proved. The AHH algorithm is developed similar to the MARS algorithm. It is adaptive and can be executed efficiently, hence has power and flexibility to model unknown relationships. The AHH procedure is applied to identifying two dynamic systems and its potential is illustrated.

KW - Adaptive regression

KW - Identification methods

KW - Piecewise-linear

KW - System model validation

UR - https://www.scopus.com/pages/publications/70049106925

U2 - 10.1016/j.automatica.2009.06.013

DO - 10.1016/j.automatica.2009.06.013

M3 - 文章

AN - SCOPUS:70049106925

SN - 0005-1098

VL - 45

SP - 2325

EP - 2332

JO - Automatica

JF - Automatica

IS - 10

ER -

Adaptive hinging hyperplanes and its applications in dynamic system identification

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this