## $$\mathcal L_{2}-\mathcal L_{\infty }$$ nonlinear system identification via recurrent neural networks.(English)Zbl 1209.93035

Summary: This paper proposes an $$\mathcal L_{2}-\mathcal L_{\infty }$$ 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 $$\mathcal L_{2}-\mathcal L_{\infty }$$ learning algorithm is presented to reduce the effect of disturbance to an $$\mathcal L_{2}-\mathcal L_{\infty }$$ 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 $$\mathcal L_{2}-\mathcal L_{\infty }$$ 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:

 93B30 System identification 93B36 $$H^\infty$$-control

LMI toolbox
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### References:

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