Adaptive Identification Of Nonlinear System Based On ESN

The paper discusses the mechanism of nonlinear dynamical systems' identification and of the prediction of chaotic time series. The presence of noise in the identification of nonlinear dynamical systems has broken the internal chaotic dynamics of the systems and influenced the identification of nonlinear dynamical systems and the prediction of the chaotic time series. Therefore, it's necessary for us to study the noise smoothing methods of chaotic time series effectively before we do the identification and prediction of the chaotic time series. Local average nonlinear noise reduction method has been presented to deduct the noise. It can correct the position of the data points in phase space better and approximate the real chaotic attractor trajectories more closely. The computation is simple and credible. The simulation has proven the validity of the method to provide the basic condition for the identification and prediction of the chaotic nonlinear dynamical systems. For traditional identification methods just use fixed data to establish fixed prediction mode, an online adaptive prediction method of chaotic time series is proposed to conquer the disadvantages above-mentioned. ESN (Echo state network) is a new type of RNN (recurrent neural network) based on the "reservoir". It can be effectively used in nonlinear dynamical systems' identification and the prediction of chaotic time series. The mechanism of reservoir simply uses linear method to solve the problem of the nonlinear system. This arithmetic of prediction is easier than traditional RNN. This paper base on the theorem of Takens and reconstructs phase space of chaotic time series embedded in a phase space of appropriate dimensions. It selects ESN with the mechanism of the "reservoir" as predict model to set up a direct predict method which directly relates the prediction origin and prediction horizon. The method respectively use the optimal state estimation algorithm of Kalman Filter(KF) and Least Mean Square(LMS) to estimate the signal in linear part to refresh the parameters of the model. Applying the method to the prediction of monthly sunspots, the simulation has proven it effective to apply to the online identification of chaotic time series.