ℒ₂-ℒ_∞ nonlinear system identification via recurrent neural networks

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.