L2–L∞ learning of dynamic neural networks

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

中国物理B ›› 2010, Vol. 19 ›› Issue (10): 100201-100201.doi: 10.1088/1674-1056/19/10/100201

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L₂–L_∞ 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

收稿日期:2009-11-21 修回日期:2010-04-05 出版日期:2010-10-15 发布日期:2010-10-15
基金资助:
Project supported by the Grant of the Korean Ministry of Education, Science and Technology (The Regional Core Research Program/Center for Healthcare Technology Development).

$\mathscr{L}$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

Received:2009-11-21 Revised:2010-04-05 Online:2010-10-15 Published:2010-10-15
Supported by:
Project supported by the Grant of the Korean Ministry of Education, Science and Technology (The Regional Core Research Program/Center for Healthcare Technology Development).

摘要/Abstract

摘要： 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.

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.

Key words: $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ learning law, dynamic neural networks, linear matrix inequality, Lyapunov stability theory

中图分类号: (Matrix theory)

02.10.Yn

02.30.Yy (Control theory) 07.05.Mh (Neural networks, fuzzy logic, artificial intelligence)

Choon Ki Ahn. L₂–L_∞ learning of dynamic neural networks[J]. 中国物理B, 2010, 19(10): 100201-100201.

Choon Ki Ahn. $\mathscr{L}$₂–$\mathscr{L}$_$\infty$ learning of dynamic neural networks[J]. Chin. Phys. B, 2010, 19(10): 100201-100201.

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L₂–L_∞ learning of dynamic neural networks

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

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