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Recurrent neurofuzzy networks have proven to be useful in identification of systems with unknown dynamics when only input–output information is available. However, training algorithms for these structures usually require also the measurement of the actual states of the system in order to obtain a convergent algorithm and then obtain a scheme to approximate its dynamic behavior. When states are not available and only input–output information can be obtained, the stability of the training algorithm of the recurrent networks is hard to establish, as the dynamics is driven by the internal recurrent dynamics of each connection. In this paper, we present a structure and an ultimately stable training algorithm inspired by adaptive observer for black-box identification based on state-space recurrent neural networks for a class of dynamic nonlinear systems in discrete-time. The network catches the dynamics of the unknown plant and jointly identifies its parameters using only output measurements, with ultimately bounded identification and parameter error. Numerical examples using simulated and experimental systems are included to illustrate the effectiveness of the proposed method. |
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