Research On Adaptive Prediction Method Of Time Series

Time series forecasting has important practical value and significance in engineeringapplications. According to the input and output data，adaptive control can identify the modelstructure and parameters constantly. Thus，it can modify the characteristics to adapt thechanges in objects and disturbance dynamics.In this paper, the advanced methods of adaptivecontrol were applied to time series prediction. In order to improve forecast accuracy, the linear,nonlinear and chaotic time series were studied respectively.For linear time series, the adaptive control method to predict linear time series isresearched in the paper. Slow varying parameters adaptive model，parameters adaptive modeland minimum variance self-tuning prediction model are designed.The gradient method andLyapunov method is used in the slow varying parameters adaptive model. The CARMA isused and its parameters are adjusted adaptively in the parameters adaptive model. Thed steps ahead forecast is used and its adaptive control law is designed in the minimumvariance self-tuning prediction model.For the non-uniform target problem in the high-order nonlinear systems with unknowncontrol coefficient,an adaptive algorithm of iterative learning control and hybrid parameter isproposed. The improved backstepping method, recombination parameters and segmentedconstructing Lyapunov function are applied in this algorithm.At the same time, the invariantparameter adaptive law，adaptive control law，and time-varying parameter vector adaptive laware designed in turn. So the non-uniform target problem can be solved. By constructing aLyapunov-like functional, the error converges is proved to be zero and all signals are provedto be bounded.For a problem of adaptive generalized projective synchronization with unknown timevarying parameter periods，a periods identification algorithm based on switching logic isproposed in this paper. First, the known the periods of time-varying parameters is assumed.the adaptive controller and the time-varying parameter adaptive law are designed. Secondly,the reasonable switching logic is designed. Thirdly, the period range of parameter is locatedby the average error between two iterations. The periods of parameter is located by theaccumulative tracking error. Finally, the synchronization of two chaotic systems is completed.By constructing a Lyapunov-Krasovskii functional，the error converges is proved to be zeroand all signals are proved to be bounded.