本論文運用資訊理論的指標與原理—熵與最大熵值原理，來研究精密機械系統的動態響應與系統穩定性等相關的問題。為了定性與定量地分析相互作用複雜的精密機械系統的輸入輸出關係，以及作為接下來結構設計和控制系統設計的基礎，本論文首先以一個非線性隨機微分方程式，來模擬整個精密機械系統的動態響應行為。由於一般非線性隨機微分方程式低階矩函數的演化方程式，通常藕合著更高階的矩函數而形成無窮層級地交鎖；因此造成系統動態響應解析困難，更遑論及系統穩定性方面的探討。而在本文中根據熵模態的分解提出一個資訊閉合方法，能夠在現有的低次矩與高次矩函數或是系統矩函數相關方程式之資訊拘束條件下，透過資訊理論的最大熵值原理，近似地解析求得非線性隨機系統的動態響應之演化過程及分析系統的隨機穩定性。

　　其次透過所發展的資訊閉合方法，本論文提出一個新的統計線性化方法來預測非線性隨機系統的動態輸出響應。根據資訊閉合法所求得的精確機率密度函數，此資訊閉合統計線性化法所建立的等效線性模型，具有精確地預測非線性隨機系統的動態輸出響應的特性；此外，還可以再利用資訊閉合方法所估測的系統熵值上界，來調整資訊閉合統計線性化模型的外在激擾強度，使模型的熵值響應能保證為原非線性隨機系統熵值響應的上界。此種具有系統熵值上界特性之線性化模型，可以用在非線性隨機系統如具隨機激擾或有不確定交互作用之精密機械系統的強健性響應分析與控制設計上。

　　本論文除了理論推導外，更提出數個例子來展示資訊閉合方法與資訊閉合統計線性化方法之各種應用，包括在非線性隨機系統的隨機穩定性、最佳控制、強健分析與強健設計上之應用。最後並將這些方法實際運用在一個精密設備移動平台之防震控制系統的動態分析與結構和控制整合之設計上。

　　In this dissertation, dynamic responses and robust stability of precision mechanical systems are studied by the entropy index of information theory. The dynamic evolution behavior of the precision mechanical systems and the random interactions with their environments are modeled and expressed as nonlinear stochastic differential equations with disturbances for the following response analysis or control design.

　　Owing to the inevitably hierarchical coupled moment equations of the nonlinear stochastic differential equations, it is very difficult to obtain exactly dynamic responses, let alone stability analysis, of the nonlinear stochastic systems. An information closure method based on the available moment information or the moment-relation equations is proposed to overcome these difficulties. By the way of entropy mode decomposition and the maximum entropy principle of information theory, the closure method can be utilized to obtain analytically not only the dynamic responses but also the robust stability boundary of the nonlinear stochastic systems.

　　Based on the information closure method, a new statistical linearization method is proposed. Accurate dynamic responses and entropy upper bound of nonlinear stochastic systems can be predicted by the information-closure linearization method. Moreover, the intensities of the external noises of the linearization model can be further modified so that the entropy of the resulted model is guaranteed as the upper bound of that estimated by the closure method. The guaranteed property makes come true the robust design of the nonlinear stochastic systems in entropy sense.

　　Several examples, including the analysis of stochastic stability, the design of optimal control, and the design of robust control, are also given for the illustrations of the applications of the information closure method and the information-closured linearization method. Finally, these methods are actually employed in the dynamic analysis and the integrated design of a precise carry plant.

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