ℒ2–ℒ∞ nonlinear system identification via recurrent neural networks
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- Ahn, C.K. Nonlinear Dyn (2010) 62: 543. doi:10.1007/s11071-010-9741-3
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.