Research On Adaptive Prediction Method For Chaotic Time Series

As nonlinear dynamical system, chaos systems always have uncertain or incomplete system information. Because of its extreme sensitivity to initial conditions and that it has strange attractor, it is difficult to establish a precise mathematical model. According to the current available data and prediction error, adaptive control can adjust parameters constantly. Thus, it can adapt to the time-vary system or system with incomplete data. In this paper, adaptive control is applied to chaotic time series forecasting and adaptive prediction model is established. The main contents of this paper are as follows:First the reconstruction of phase space and discrimination of time series chaotic characteristic are studied. For the reconstruction of phase space, selection of the delay time and embedding dimension are mainly discussed. The delay time is determined by the method of auto correlation and mutual information, and the embedding dimension is determined by saturation correlation dimension and Cao method. For the discrimination of time series chaotic characteristic, it is mainly determined from the qualitative and quantitative aspect, ultimately the discrimination of time series is achieved.In order to solve the limitations of traditional mode, such as no ability to learn, low accuracy and slow convergence, the adaptive prediction of volterra model based on fractional least mean square(FLMS) algorithm is proposed. The FLMS algorithm is introduced by adding a fractional derivative term in the standard least mean square(LMS) algorithm to improve the convergence of the algorithm. Meanwhile, a modified fractional least mean square algorithm is introduced by adding the adjustable gain parameter to simplify the operation speed of algorithm. Finally, the results of simulation experiments are compared to demonstrate the superiority of the proposed algorithm.The prediction model of chaotic time with time-varying parameter is resolved by designing rational control law and time-vary parameter adaptive learning law with fractional item. Meanwhile, in order to improve the algorithm’s prediction accuracy and convergence speed, simulated annealing(SA) algorithm is proposed to optimize the time-vary parameter adaptive learning law. Finally the prediction of chaotic time with time-varying parameter is completed. The effectiveness of the proposed algorithm is illustrated by the simulation results.