$\mathscr{L}$2–$\mathscr{L}$$\infty$ learning of dynamic neural networks

doi:10.1088/1674-1056/19/10/100201

Abstract This paper proposes an $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ learning law as a new learning method for dynamic neural networks with external disturbance. Based on linear matrix inequality (LMI) formulation, the $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ learning law is presented to not only guarantee asymptotical stability of dynamic neural networks but also reduce the effect of external disturbance to an $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ induced norm constraint. It is shown that the design of the $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ 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: $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ 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 $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ 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

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$\mathscr{L}$₂–$\mathscr{L}$_$\infty$ learning of dynamic neural networks