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Zbl 1209.93035
Ahn, Choon Ki
$\cal L_{2}-\cal L_{\infty }$ nonlinear system identification via recurrent neural networks. (English)
[J] Nonlinear Dyn. 62, No. 3, 543-552 (2010). ISSN 0924-090X; ISSN 1573-269X/e

Summary: This paper proposes an $\cal L_{2}-\cal L_{\infty }$ identification scheme as a new robust identification method for nonlinear systems via recurrent neural networks. Based on linear matrix inequality (LMI) formulation, for the first time, the $\cal L_{2}-\cal L_{\infty }$ learning algorithm is presented to reduce the effect of disturbance to an $\cal L_{2}-\cal L_{\infty }$ induced norm constraint. New stability results, such as boundedness, input-to-state stability (ISS), and convergence, are established in some senses. It is shown that the design of the $\cal L_{2}-\cal L_{\infty }$ identification method 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 identification scheme.

MSC 2000:: *93B30 System identification
93B36 $H^\infty$-control

Keywords: $\cal L_{2}-\cal L_{\infty }$ identification; recurrent neural networks; input-to-state stability (ISS); linear matrix inequality (LMI); weight learning law

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Zentralblatt MATH Berlin [Germany]