Self-organizing radial basis function network for real-time approximation of continuous-time dynamical systems

Jianming Lian; Yonggon Lee; Scott D. Sudhoff; Stanislaw H. Zak

doi:10.1109/TNN.2007.909842

Self-organizing radial basis function network for real-time approximation of continuous-time dynamical systems

Jianming Lian
, Yonggon Lee
, Scott D. Sudhoff
, Stanislaw H. Zak

Grid-Interactive Controls

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

75 Scopus citations

Abstract

Real-time approximators for continuous-time dynamical systems with many inputs are presented. These approximators employ a novel self-organizing radial basis function (RBF) network, which varies its structure dynamically to keep the prescribed approximation accuracy. The RBFs can be added or removed online in order to achieve the appropriate network complexity for the real-time approximation of the dynamical systems and to maintain the overall computational efficiency. The performance of this variable structure RBF network approximator with both Gaussian RBF (GRBF) and raised-cosine RBF (RCRBF) is analyzed. The compact support of RCRBF enables faster training and easier output evaluation of the network than that of the network with GRBF. The proposed real-time self-organizing RBF network approximator is then employed to approximate both linear and nonlinear dynamical systems to illustrate the effectiveness of our proposed approximation scheme, especially for higher order dynamical systems. The uniform ultimate boundedness of the approximation error is proved using the second method of Lyapunov.

Original language	English
Pages (from-to)	460-474
Number of pages	15
Journal	IEEE Transactions on Neural Networks
Volume	19
Issue number	3
DOIs	https://doi.org/10.1109/TNN.2007.909842
State	Published - Mar 2008

Funding

Manuscript received January 26, 2007; revised June 4, 2007 and July 17, 2007; accepted July 18, 2007. This work was supported by the Office of Naval Research under Grant N00014-02-1-0623. J. Lian, S. D. Sudhoff, and S. H. Żak are with the School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA (e-mail: [email protected]; [email protected]; [email protected]). Y. Lee is with the Weapons and Systems Engineering Department, United States Naval Academy, Annapolis, MD 21402 USA (e-mail: [email protected]). Digital Object Identifier 10.1109/TNN.2007.909842

Keywords

Dynamical system
Gaussian RBF (GRBF)
Radial basis function (RBF)
Raised-cosine RBF (RCRBF)
Real-time approximation
Self-organizing RBF network
Uniform ultimate boundedness

Access to Document

10.1109/TNN.2007.909842

Cite this

@article{414788457f9640beb140f8ca7afe29d1,

title = "Self-organizing radial basis function network for real-time approximation of continuous-time dynamical systems",

abstract = "Real-time approximators for continuous-time dynamical systems with many inputs are presented. These approximators employ a novel self-organizing radial basis function (RBF) network, which varies its structure dynamically to keep the prescribed approximation accuracy. The RBFs can be added or removed online in order to achieve the appropriate network complexity for the real-time approximation of the dynamical systems and to maintain the overall computational efficiency. The performance of this variable structure RBF network approximator with both Gaussian RBF (GRBF) and raised-cosine RBF (RCRBF) is analyzed. The compact support of RCRBF enables faster training and easier output evaluation of the network than that of the network with GRBF. The proposed real-time self-organizing RBF network approximator is then employed to approximate both linear and nonlinear dynamical systems to illustrate the effectiveness of our proposed approximation scheme, especially for higher order dynamical systems. The uniform ultimate boundedness of the approximation error is proved using the second method of Lyapunov.",

keywords = "Dynamical system, Gaussian RBF (GRBF), Radial basis function (RBF), Raised-cosine RBF (RCRBF), Real-time approximation, Self-organizing RBF network, Uniform ultimate boundedness",

author = "Jianming Lian and Yonggon Lee and Sudhoff, \{Scott D.\} and Zak, \{Stanislaw H.\}",

year = "2008",

month = mar,

doi = "10.1109/TNN.2007.909842",

language = "English",

volume = "19",

pages = "460--474",

journal = "IEEE Transactions on Neural Networks",

issn = "1045-9227",

number = "3",

}

TY - JOUR

T1 - Self-organizing radial basis function network for real-time approximation of continuous-time dynamical systems

AU - Lian, Jianming

AU - Lee, Yonggon

AU - Sudhoff, Scott D.

AU - Zak, Stanislaw H.

PY - 2008/3

Y1 - 2008/3

N2 - Real-time approximators for continuous-time dynamical systems with many inputs are presented. These approximators employ a novel self-organizing radial basis function (RBF) network, which varies its structure dynamically to keep the prescribed approximation accuracy. The RBFs can be added or removed online in order to achieve the appropriate network complexity for the real-time approximation of the dynamical systems and to maintain the overall computational efficiency. The performance of this variable structure RBF network approximator with both Gaussian RBF (GRBF) and raised-cosine RBF (RCRBF) is analyzed. The compact support of RCRBF enables faster training and easier output evaluation of the network than that of the network with GRBF. The proposed real-time self-organizing RBF network approximator is then employed to approximate both linear and nonlinear dynamical systems to illustrate the effectiveness of our proposed approximation scheme, especially for higher order dynamical systems. The uniform ultimate boundedness of the approximation error is proved using the second method of Lyapunov.

AB - Real-time approximators for continuous-time dynamical systems with many inputs are presented. These approximators employ a novel self-organizing radial basis function (RBF) network, which varies its structure dynamically to keep the prescribed approximation accuracy. The RBFs can be added or removed online in order to achieve the appropriate network complexity for the real-time approximation of the dynamical systems and to maintain the overall computational efficiency. The performance of this variable structure RBF network approximator with both Gaussian RBF (GRBF) and raised-cosine RBF (RCRBF) is analyzed. The compact support of RCRBF enables faster training and easier output evaluation of the network than that of the network with GRBF. The proposed real-time self-organizing RBF network approximator is then employed to approximate both linear and nonlinear dynamical systems to illustrate the effectiveness of our proposed approximation scheme, especially for higher order dynamical systems. The uniform ultimate boundedness of the approximation error is proved using the second method of Lyapunov.

KW - Dynamical system

KW - Gaussian RBF (GRBF)

KW - Radial basis function (RBF)

KW - Raised-cosine RBF (RCRBF)

KW - Real-time approximation

KW - Self-organizing RBF network

KW - Uniform ultimate boundedness

UR - https://www.scopus.com/pages/publications/41049101978

U2 - 10.1109/TNN.2007.909842

DO - 10.1109/TNN.2007.909842

M3 - Article

C2 - 18334365

AN - SCOPUS:41049101978

SN - 1045-9227

VL - 19

SP - 460

EP - 474

JO - IEEE Transactions on Neural Networks

JF - IEEE Transactions on Neural Networks

IS - 3

ER -

Self-organizing radial basis function network for real-time approximation of continuous-time dynamical systems

Abstract

Funding

Keywords

Access to Document

Other files and links

Fingerprint

Cite this