運用功率譜估測法及類神經網來做混沌系統識別

Abstract

此論文中，兩種模式化方法被發展在混沌系統(chaotic system)的識別上 。一種是運用隨機線性模式化的方法，它是利用以模式為基礎的功率譜估 測法以找出功率譜近似的馬可夫模式。此方法是由白色雜音所驅動馬可夫 模式使得其輸出功率譜非常趨近原來信號功率譜。此法要點是找出一個功 率譜因子及其相關的分時雷卡地方程式(discrete-time algebraic Riccati equation)，解此方程式則可得到功率譜近似的馬可夫動態方程 式。此法的好處在於系統化和簡易化的得到馬可夫動態方程式。另一種是 決定性的非線性模式化方法，它是利用類神經網路來做混沌系統識別。串 並聯模式能描述混沌系統的動態，但其所追蹤的資料必須被要求具有穩健 性的缺點。並聯模式能維持混沌系統部分資訊，但卻無法追蹤資料的缺點 。一種新模式被提出以解決串並聯模式及並聯模式的 In this thesis, two modeling methodologies are developed for the identification of discrete-time chaotic systems. One of thodologies is linear stochastic modeling utilizing the model- based spectral estimation to find a spectrum-approximated Markovian model. The approach is related to a Markovian representation such that the power spectrum of the estimated output is very close to the power spectrum of the original one. This approach is that by solvingdiscrete-time algebraic Riccati equation associated with the system matrices of the Markovian model, we can have the system dynamics. The novelty of this approach is to get system dynamics systematically and much easier. The other modeling methodologies is nonlinear deterministic modeling using neural networks to model a discrete-time chaotic system. A Series-Parallel Model can decribe the system dynamics but its tracking data must always be allowable. A Parallel Model can hold partial system dynamics, but it can't track data well. A new model, called Novel Model,can overcome disadvantages of the Parallel Model and the Series-Parallel Model.