ℒ2–ℒ∞ nonlinear system identification via recurrent neural networks
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This paper proposes an ℒ2–ℒ∞ 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 ℒ2–ℒ∞ learning algorithm is presented to reduce the effect of disturbance to an ℒ2–ℒ∞ 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 ℒ2–ℒ∞ 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.
Keywordsℒ2–ℒ∞ identification Recurrent neural networks Input-to-state stability (ISS) Linear matrix inequality (LMI) Weight learning law
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