Please wait a minute...
ZJUS-A
Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering)  2008, Vol. 9 Issue (8): 1015-1023    DOI: 10.1631/jzus.A0720122
Electrical & Electronic Engineering     
A new neural network model for the feedback stabilization of nonlinear systems
Mei-qin LIU, Sen-lin ZHANG, Gang-feng YAN
School of Electrical Engineering, Zhejiang University, Hangzhou 310027, China
Download:     PDF (0 KB)     
Export: BibTeX | EndNote (RIS)      

Abstract  A new neural network model termed ‘standard neural network model’ (SNNM) is presented, and a state-feedback control law is then designed for the SNNM to stabilize the closed-loop system. The control design constraints are shown to be a set of linear matrix inequalities (LMIs), which can be easily solved by the MATLAB LMI Control Toolbox to determine the control law. Most recurrent neural networks (including the chaotic neural network) and nonlinear systems modeled by neural networks or Takagi and Sugeno (T-S) fuzzy models can be transformed into the SNNMs to be stabilization controllers synthesized in the framework of a unified SNNM. Finally, three numerical examples are provided to illustrate the design developed in this paper.

Key words： Standard neural network model (SNNM)      Linear matrix inequality (LMI)      Nonlinear control      Asymptotic stability      Chaotic cellular neural network      Takagi and Sugeno (T-S) fuzzy model     
Received: 13 December 2007     
CLC:  TP273  
Service
E-mail this article
Add to my bookshelf
Add to citation manager
E-mail Alert
RSS
Articles by authors
Mei-qin LIU
Sen-lin ZHANG
Gang-feng YAN
Cite this article:

Mei-qin LIU, Sen-lin ZHANG, Gang-feng YAN. A new neural network model for the feedback stabilization of nonlinear systems. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(8): 1015-1023.

URL:

http://www.zjujournals.com/xueshu/zjus-a/10.1631/jzus.A0720122     OR     http://www.zjujournals.com/xueshu/zjus-a/Y2008/V9/I8/1015

[1] Hui-jiao WANG, Xiao-dong ZHAO, An-ke XUE, Ren-quan LU. Delay-dependent robust control for uncertain discrete singular systems with time-varying delay[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(8): 1034-1042.
[2] Deng-feng ZHANG, Hong-ye SU, Jian CHU, Zhi-quan WANG. Suboptimal reliable guaranteed cost control for continuous-time systems with multi-criterion constraints[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(8): 1024-1033.
[3] Wei QIAN, Guo-jiang SHEN, You-xian SUN. Dynamical output feedback stabilization for neutral systems with mixed delays[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(8): 1043-1049.
[4] Chang-fei TONG, Hui ZHANG, You-xian SUN. Control synthesis for polynomial nonlinear systems and application in attitude control[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(6): 833-839.
[5] Hui-jiao WANG, An-ke XUE, Yun-fei GUO, Ren-quan LU. Input-output approach to robust stability and stabilization for uncertain singular systems with time-varying discrete and distributed delays[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(4): 546-551.
[6] Mei-qin LIU, Jian-hai ZHANG. Exponential synchronization of general chaotic delayed neural networks via hybrid feedback[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2008, 9(2): 262-270.
[7] CHEN Yun, XUE An-ke, GE Ming, WANG Jian-zhong, LU Ren-quan. On exponential stability for systems with state delays[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(8): 1296-1303.
[8] SREEKUMAR M., SINGAPERUMAL M., NAGARAJAN T., ZOPPI M., MOLFINO R.. Recent advances in nonlinear control technologies for shape memory alloy actuators[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(5): 818-829.
[9] ZHANG Jian-hai, ZHANG Sen-lin, LIU Mei-qin. Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2007, 8(12): 1912-1920.
[10] Liu Mei-Qin. Stability analysis of neutral-type nonlinear delayed systems: An LMI approach[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(Supplement 2): 237-244.
[11] Liu Mei-qin. Interval standard neural network models for nonlinear systems[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(4 ): 8-.
[12] BAI Lei-shi, HE Li-ming, TIAN Zuo-hua, SHI Song-jiao. Design of H∞ robust fault detection filter for nonlinear time-delay systems[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2006, 7(10): 16-.
[13] ZHANG Sen-lin, LIU Mei-qin. Stability analysis of discrete-time BAM neural networks based on standard neural network models*[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 7): 14-.
[14] ZHANG Sen-lin, LIU Mei-qin. LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2005, 6( 1): 5-.
[15] CAO Feng-wen, LU Ren-quan, SU Hong-ye, CHU Jian. Robust H∞ output feedback control for a class of uncertain Lur’e systems with time-delays[J]. Journal of Zhejiang University-SCIENCE A (Applied Physics & Engineering), 2004, 5( 9): 14-.