Please use this identifier to cite or link to this item: `http://hdl.handle.net/11455/8344`
 標題: 估測、適應控制與系統分析之訊息理論方法Estimation, Adaptive Control and System Analysis: An Information Theoretic Approach 作者: 陳益生 關鍵字: Entropy;熵數;Information Theory;Kalman filter;adaptive optimal control;system analysis;estimation;訊息理論;卡爾曼濾波器;最佳適應控制;系統分析;估測 出版社: 電機工程學系 摘要: 本論文旨在利用訊息理論的方法來研究最佳狀態估測、離散時間最佳適應控制，以及系統分析等三類問題。 對於連續及取樣時間的線性高斯系統而言，滿足傳統最小誤差平方量測的卡爾曼濾波器在本文所定義的四種訊息理論量測上同時也是最佳的。而最小熵數誤差的研究只有在濾波器是無偏的情況下才有意義。針對線性高斯系統，最小誤差熵數濾波器可以類似卡爾曼濾波法則推導出。 對於隨機與非隨機的離散時間最佳適應控制問題而言，一有意義的熵數表示式被詳細地推導，其物理意涵也被詳細解釋。此結果說明：最佳總熵數同時也就是整個系統的代價函數，而此最佳代價函數等於傳統確定等義原則下的適應控制之熵數減去系統控制所造成的不確定熵數。 本文最後提出能夠分析系統結構與輸入的訊息理論分解法則。分解式中的各訊息項可被賦予相對應的物理涵義。隨後舉出兩個例子來說明此訊息理論分解公式的應用。This thesis uses information theoretic approach to study the problems of optimal state estimation, discrete-time adaptive optimal control and some system analysis issues. For continuous time and sampled data linear Gaussian systems, it is proved that Kalman filters are the optimal filters not only for minimum mean square error measure, but also for the information theoretic measures introduced in the thesis. The investigation of minimum error entropy is meaningful only when the filter is unbiased. A Kalman-filter-like algorithm to a minimum error entropy filter for a linear Gaussian system is presented. Entropy formulations for deterministic and stochastic adaptive optimal control problems are derived. The resulting expressions are derived in detail and their physical meanings are provided. These results show that the minimum (optimal) cost function which is the same as the total entropy of the system is equal to the cost (entropy) of adaptive control minus the equivocation of the knowledge that the system is controlled. Three information partition laws for systems and input are developed and their physical meanings are interpreted. Two examples are used for illustration of implications of the proposed laws. URI: http://hdl.handle.net/11455/8344 Appears in Collections: 電機工程學系所

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