Please wait a minute...
Chin. Phys. B, 2010, Vol. 19(10): 100201    DOI: 10.1088/1674-1056/19/10/100201
GENERAL   Next  

L2L learning of dynamic neural networks

Choon Ki Ahn
Department of Automotive Engineering, Seoul National University of Technology, 172 Gongneung 2-dong, Nowon-gu, Seoul 139-743, Korea
Abstract  This paper proposes an L2L learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the L2L learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an L2L induced norm constraint. It is shown that the design of the L2L learning law for such neural networks can be achieved by solving LMIs, which can be easily facilitated by using some standard numerical packages. A numerical example is presented to demonstrate the validity of the proposed learning law.
Keywords:  L2L learning law      dynamic neural networks      linear matrix inequality      Lyapunov stability theory   
Received:  21 November 2009      Revised:  05 April 2010      Accepted manuscript online: 
PACS:  02.10.Yn (Matrix theory)  
  02.30.Yy (Control theory)  
  07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)  
Fund: Project supported by the Grant of the Korean Ministry of Education, Science and Technology (The Regional Core Research Program/Center for Healthcare Technology Development).

Cite this article: 

Choon Ki Ahn L2L learning of dynamic neural networks 2010 Chin. Phys. B 19 100201

[1] Gupta M M, Jin L and Homma N 2003 Static and Dynamic Neural Networks (New York: Wiley-Interscience)
[2] Liang X B and Wu L D 1998 IEEE Trans. Circuits Syst. I 45 1010
[3] Sanchez E and Perez J P 1999 IEEE Trans. Circuits Syst. I 46 1395
[4] Hu S and Wang J 2003 IEEE Trans. Neural Networks 14 35
[5] Chu T, Zhang C and Zhang Z 2003 Neural Networks 16 1223
[6] Chu T and Zhang C 2007 Neural Networks 20 94
[7] Rovithakis G and Christodoulou M 1994 IEEE Trans. Syst., Man, Cybern. 24 400
[8] Jagannathan S and Lewis F 1996 Automatica 32 1707
[9] Suykens J A K, Vandewalle J and Moor B D 1997 IEEE Trans. Signal Process. 45 2682
[10] Yu W and Li X 2001 IEEE Trans. Circuits Syst. I 48 256
[11] Chairez I, Poznyak A and Poznyak T 2006 IEEE Trans. Circuits Syst. II 53 1338
[12] Yu W and Li X 2007 Neural Processing Letters 25 143
[13] Rubio and Yu W 2007 Neurocomputing 70 2460
[14] Grigoriadis K and Watson J 1997 IEEE Trans. Aerosp. Electron. Syst. 33 1326
[15] Watson J and Grigoriadis K 1998 Systems and Control Letters 35 111
[16] Palhares R and Peres P 2000 Automatica 36 851
[17] Gao H and Wang C 2003 IEEE Trans. Trans. Circ. Syst. I 50 594
[18] Gao H and Wang C 2003 IEEE Trans. Automat. Control 48 1661
[19] Mahmoud M 2007 IET Control Theory and Applications 1 141
[20] Qiu J, Feng G and Yang J 2008 IET Control Theory and Applications 2 795
[21] Zhou Y and Li J 2008 IET Control Theory and Applications 2 773
[22] Boyd S, Ghaoui L E, Feron E and Balakrishinan V 1994 Linear Matrix Inequalities in Systems and Control Theory (Philadelphia: SIAM)
[23] Gahinet P, Nemirovski A, Laub A J and Chilali M 1995 LMI Control Toolbox (Natick: The Mathworks Inc.)
[24] Hopfield J 1984 Proc. Nat. Acad. Sci. 81 3088
[25] Wilson D 1989 IEEE Trans. Automat. Control 34 94
[26] Skelton R, Iwasaki T and Grigoriadis K 1997 A Unified Algebraic Approach to Linear Control Design (London: Taylor & Francis)
[27] Hunt K, Sbarbaro D, Zbikowski R and Gawthrop P 1992 Automatica 28 1083
[1] Adaptive synchronization of chaotic systems with less measurement and actuation
Shun-Jie Li(李顺杰), Ya-Wen Wu(吴雅文), and Gang Zheng(郑刚). Chin. Phys. B, 2021, 30(10): 100503.
[2] Robust H control for uncertain Markovian jump systems with mixed delays
R Saravanakumar, M Syed Ali. Chin. Phys. B, 2016, 25(7): 070201.
[3] Robust H control of uncertain systems with two additive time-varying delays
M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2015, 24(9): 090202.
[4] Chaotic synchronization in Bose–Einstein condensate of moving optical lattices via linear coupling
Zhang Zhi-Ying (张志颖), Feng Xiu-Qin (冯秀琴), Yao Zhi-Hai (姚治海), Jia Hong-Yang (贾洪洋). Chin. Phys. B, 2015, 24(11): 110503.
[5] Stability analysis of Markovian jumping stochastic Cohen–Grossberg neural networks with discrete and distributed time varying delays
M. Syed Ali. Chin. Phys. B, 2014, 23(6): 060702.
[6] Improved delay-dependent robust H control of an uncertain stochastic system with interval time-varying and distributed delays
M. Syed Ali, R. Saravanakumar. Chin. Phys. B, 2014, 23(12): 120201.
[7] Cluster exponential synchronization of a class of complex networks with hybrid coupling and time-varying delay
Wang Jun-Yi (王军义), Zhang Hua-Guang (张化光), Wang Zhan-Shan (王占山), Liang Hong-Jing (梁洪晶). Chin. Phys. B, 2013, 22(9): 090504.
[8] Stability analysis and control synthesis of uncertain Roesser-type discrete-time two-dimensional systems
Wang Jia (王佳), Hui Guo-Tao (会国涛), Xie Xiang-Peng (解相朋). Chin. Phys. B, 2013, 22(3): 030206.
[9] Novel delay dependent stability analysis of Takagi–Sugeno fuzzy uncertain neural networks with time varying delays
M. Syed Ali . Chin. Phys. B, 2012, 21(7): 070207.
[10] Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions
Dai Hao (戴浩), Jia Li-Xin (贾立新), Zhang Yan-Bin (张彦斌). Chin. Phys. B, 2012, 21(12): 120508.
[11] Novel delay-distribution-dependent stability analysis for continuous-time recurrent neural networks with stochastic delay
Wang Shen-Quan (王申全), Feng Jian (冯健), Zhao Qing (赵青). Chin. Phys. B, 2012, 21(12): 120701.
[12] Robust H control for uncertain systems with heterogeneous time-varying delays via static output feedback
Wang Jun-Wei (王军威), Zeng Cai-Bin (曾才斌 ). Chin. Phys. B, 2012, 21(11): 110206.
[13] Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique
Feng Yi-Fu (冯毅夫), Zhang Qing-Ling (张庆灵), Feng De-Zhi (冯德志). Chin. Phys. B, 2012, 21(10): 100701.
[14] Robust stability analysis of Takagi–Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays
M. Syed Ali . Chin. Phys. B, 2011, 20(8): 080201.
[15] A novel mixed-synchronization phenomenon in coupled Chua's circuits via non-fragile linear control
Wang Jun-Wei(王军威), Ma Qing-Hua(马庆华), and Zeng Li(曾丽) . Chin. Phys. B, 2011, 20(8): 080506.
No Suggested Reading articles found!