運用以類神經網路為基礎的卡門濾波器模式化混沌系統

Abstract

在本論文中，我們利用線性及非線性兩種模式從時間序列角度來處理系統估測問題。在線性系統中，我們提出幾何方法及自我遞迴模式，以此兩種方法、模式所建立的估測器，其輸出值為過去幾個真正系統輸出值加權後的線性組合。在非線性系統中，我們利用類神經網路做系統辨別（system ID），再以此系統辨別為基礎，發展出新的動態估測器。此類神經網路是以估測值為輸入，並且加上誤差補償器，而此誤差補償器的功能與線性卡門濾波器中的卡門增益相同，可以克服並聯模式（PM）中誤差會在疊代過程被放大的缺點。我們稱此新型動態估測器為卡門濾波器型估測器。估測結果顯示，只要系統辨別準確性夠高，即使系統處於混沌狀態（Chaotic State），此估測器亦可有良好效果。

In this paper, we deal with the prediction problem from a time series using both linear and nonlinear models. In the linear modeling, we propose the geometry method and the autoregressive model. In both models, the output of the predictor is the linear weighted combination of output of the plant. In the nonlinear modeling, we utilize the neural network to identify the dynamical system. Based on this neural network, we propose a new dynamical predictor model that the inputs of the neural network are fed with prediction values and is added with an error compensator. The error compensator, which function is the same as that of the Kalman gain in linear Kalman filter, can overcome the disadvantage of amplication of prediction error during iteration process in parallel model. We call this new dynamical predictor Kalman filter predictor. The prediction results show that even the plant is in the chaotic state, the predictor also can do good job as long as the basic identification model which is trained accurately enough.