Full Text:   <1356>

CLC number: TP183

On-line Access: 

Received: 2005-05-09

Revision Accepted: 2005-11-21

Crosschecked: 0000-00-00

Cited: 0

Clicked: 3530

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
1. Reference List
Open peer comments

Journal of Zhejiang University SCIENCE A 2006 Vol.7 No.4 P.530~538


Interval standard neural network models for nonlinear systems

Author(s):  Liu Mei-qin

Affiliation(s):  School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   liumeiqin@cee.zju.edu.cn

Key Words:  Interval standard neural network model (ISNNM), Linear matrix inequality (LMI), Nonlinear system, Asymptotic stability, Robust control

Liu Mei-qin. Interval standard neural network models for nonlinear systems[J]. Journal of Zhejiang University Science A, 2006, 7(4): 530~538.

@article{title="Interval standard neural network models for nonlinear systems",
author="Liu Mei-qin",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Interval standard neural network models for nonlinear systems
%A Liu Mei-qin
%J Journal of Zhejiang University SCIENCE A
%V 7
%N 4
%P 530~538
%@ 1673-565X
%D 2006
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.2006.A0530

T1 - Interval standard neural network models for nonlinear systems
A1 - Liu Mei-qin
J0 - Journal of Zhejiang University Science A
VL - 7
IS - 4
SP - 530
EP - 538
%@ 1673-565X
Y1 - 2006
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.2006.A0530

A neural-network-based robust control design is suggested for control of a class of nonlinear systems. The design approach employs a neural network, whose activation functions satisfy the sector conditions, to approximate the nonlinear system. To improve the approximation performance and to account for the parameter perturbations during operation, a novel neural network model termed standard neural network model (SNNM) is proposed. If the uncertainty is bounded, the SNNM is called an interval SNNM (ISNNM). A state-feedback control law is designed for the nonlinear system modelled by an ISNNM such that the closed-loop system is globally, robustly, and asymptotically stable. The control design equations are shown to be a set of linear matrix inequalities (LMIs) that can be easily solved by available convex optimization algorithms. An example is given to illustrate the control design procedure, and the performance of the proposed approach is compared with that of a related method reported in literature.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Ayala Botto, M., Wams, B., van den Boom, T., Sá da Costa, J., 2000. Robust stability of feedback linearised systems modelled with neural networks: deal with uncertainty. Engineering Applications of Artificial Intelligence, 13(6):659-670.

[2] Boyd, S.P., Ghaoui, L.E., Feron, E., Balakrishnan, V., 1994. Linear Matrix Inequalities in System and Control Theory. SIAM, Philadelphia, PA.

[3] Chandrasekharan, P.C., 1996. Robust Control of Linear Dynamical Systems. Academic Press, London.

[4] Gahinet, P., Nemirovski, A., Laub, A.J., Chilali, M., 1995. LMI Control Toolbox—For Use with Matlab. The Math Works Inc., Natick, MA.

[5] Hunt, K.J., Sbarbaro, D., Zbikowski, R., Gawthrop, P.J., 1992. Neural networks for control systems—A survey. Automatica, 28(6):1083-1112.

[6] Khargonekar, P.P., Petersen, I.R., Zhou, K., 1990. Robust stabilization of uncertain linear systems: quadratic stability and H control theory. IEEE Trans. on Automatic Control, 35(3):356-361.

[7] Li, C.D., Liao, X.F., Zhang, R., 2004. Global asymptotical stability of multi-delayed interval neural networks: an LMI approach. Physics Letters A, 328(6):452-462.

[8] Limanond, S., Si, J., 1998. Neural-network-based control design: an LMI approach. IEEE Trans. on Neural Networks, 9(6):1422-1429.

[9] Lin, C.L., Lin, T.Y., 2001. An H design approach for neural net-based control schemes. IEEE Trans. on Automatic Control, 46(10):1599-1605.

[10] Moore, J.B., Anderson, B.D.O., 1968. A generalization of the Popov criterion. Journal of the Franklin Institute, 285(6):488-492.

[11] Narendra, K.S., Parthasarathy, K., 1990. Identification and control of dynamical systems using neural networks. IEEE Trans. on Neural Networks, 1(1):4-27.

[12] Rios-Patron, E., 2000. A General Framework for the Control of Nonlinear Systems. Ph.D Thesis, University of Illinois.

[13] Suykens, J.A.K., Vandewalle, J.P.L., de Moor, B.L.R., 1996. Artificial Neural Networks for Modeling and Control of Non-linear Systems. Kluwer Academic Publishers, Norwell, MA.

[14] Wams, B., Nijsse, G., van den Boom, T., 1999. A Neural-Model Based Robust Controller for Nonlinear Systems. Proceedings of the 1999 American Control Conference, 6:4066-4070.

[15] Xu, H.J., Ioannou, P.A., 2003. Robust adaptive control for a class of MIMO nonlinear systems with guaranteed error bounds. IEEE Trans. on Automatic Control, 48(5):728-742.

[16] Xu, S.Y., Lam, J., Ho, D.W.C., Zou, Y., 2004. Global robust exponential stability analysis for interval recurrent neural networks. Physics Letters A, 325(2):124-133.

[17] Zhang, S.L., Liu, M.Q., 2005. LMI-based approach for global asymptotical stability analysis of continuous BAM neural networks. Journal of Zhejiang University SCIENCE, 6A(1):32-37.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - Journal of Zhejiang University-SCIENCE