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Chin. Phys. B, 2010, Vol. 19(10): 100201    DOI: 10.1088/1674-1056/19/10/100201
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$\mathscr{L}$2–$\mathscr{L}$$\infty$ 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 $\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

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