本文提出兩種以粒子群聚最佳化法為基礎之混合式演算法，分別與NM單體搜尋法(NM-PSO)以及中心粒子群聚演算法(NM-PSO-C)做結合，針對多階最佳化問題找到最有可能的全域最佳解。
   在控制系統方面，我們以PSO演算法為基底，應用在解決不確定間隔系統數位化再設計的問題。作法上係對數位控制器參數作實數編碼後，再與不確定連續時間間隔系統數位化後之模型作結合，以閉迴路數位系統之性能做考慮，並分別以數位再設計系統頻率響應封包圖以及極值系統之增益/相位邊限的相似度為適合度評定機制之指標，藉由與其相對應之類比系統做比較，據以調整數位控制器的參數，使數位化再設計系統之性能能夠接近原類比系統。

This paper proposes hybrid optimization approaches incorporating particle swarm optimization with the use of a center particle in a swarm and an enhanced Nelder-Mead simplex search method to solve multi-dimensional optimization problems. 

Thanks to the performance of the proposed optimizer, PSO-based approaches are presented to derive optimal digital controllers for uncertain interval systems based on resemblance of extremal gain/phase margins (GM/PM) and frequency-response, respectively. By combining the uncertain plant and controller, extremal systems of the redesigned digital system having an interval plant and its continuous counterpart can be obtained as the basis for comparison. The design problem is then formulated as an optimization problem of an aggregated error function in terms of deviation on extremal GM/PM and frequency-response between the redesigned digital system and its continuous counterpart, and subsequently optimized by the proposed optimizer to obtain an optimal set of parameters for the digital controller.

中文摘要........................................I
英文摘要........................................II
致謝............................................III
目錄............................................IV
圖目錄..........................................VII
表目錄..........................................IX
第一章 前言.....................................1
第二章 演化法則.................................9
2.1	粒子群聚最佳化法.......................9
2.2	NM單體搜尋法...........................13
第三章 改良型NM單體搜尋法.......................18
3.1	擴張程序步驟之改良.....................18
3.1.1 二次擴張..................................18
3.1.2 連續擴張..................................19
3.2	縮小程序步驟之改良.....................20
3.3	改良型NM單體搜尋法之性能評估...........21

第四章 嵌入改良型NM搜尋法之混合型最佳化演算法...25
4.1	嵌入改良型NM搜尋法之粒子群聚最佳化法...26
4.2	混合型NM-PSO-CENTER最佳化法............28
4.3	模擬結果...............................31
4.3.1 比較基準..................................31
4.3.2 混合型最佳化演算法之性能評估..............36
第五章 不確定間隔系統之數位化再設計基於頻率響應之分析.....40
5.1	不確定間隔系統.........................40
5.2	間隔系統之穩定度分析...................41
5.2.1 Kharitonov 定理...........................41
5.2.2 Generalized Kharitonov 定理...............43
5.3	間隔系統之極值增益/相位邊限(GM/PM).....45
5.3.1 極值系統..................................46
5.3.2 求得極值增益/相位邊限之執行步驟...........49
5.4	以PSO演算法為基礎之數位控制器設計......52
5.4.1 以極值系統之增益/相位邊限相似度為評定機制.......52
5.4.2 以頻率響應封包圖相似度為評定機制..........56
5.5	範例...................................60
第六章 結論.....................................69
第七章 未來研究方向.............................71
參考文獻........................................73
附錄............................................81
研究著作........................................86

圖目錄
圖2.1 	粒子群聚最佳化法流程圖.................12
圖2.2	NM單體搜尋法之反射程序示意圖...........14
圖2.3 	NM單體搜尋法之擴張程序示意圖...........15
圖2.4 	(a)NM單體搜尋法之向外收縮程序示意圖....16
圖2.4 	(b)NM單體搜尋法之向內收縮程序示意圖....16
圖2.5 	(a)當 更好於 時之NM單體搜尋法之縮小程序示意圖..17
圖2.5 	(b)當 更好於 時之NM單體搜尋法之縮小程序示意圖..17
圖3.1 	二次擴張程序之示意.....................19
圖3.2 	連續擴張程序之示意圖...................20
圖4.1 	混合式NM-PSO最佳化方法之架構圖.........27
圖4.2 	混合式NM-PSO-CENTER最佳化方法之架構圖..30
圖5.1 	強健控制之系統方塊圖...................40
圖5.2 	具有不確定參數之取樣控制系統...........44
圖5.3 	取樣資料系統的閉迴路結構...............45
圖5.4 	 之Kharitonov矩形......................46
圖5.5 	以極值GM/PM為基礎之數位控制器設計方塊圖....53
圖5.6 	以頻率響應封包為基礎之數位控制器設計方塊圖..57
圖5.7 	經由PSO搜尋得到之數位控制器結合不確定連續時間間隔
      	系統數位化後之模型之頻率響應封包圖..............62
圖5.8 	各種方法所求得之數位控制器結合不確定連續時間間隔系
	統數位化後之模型之頻率響應封包圖................67
圖5.9 	隨機挑選出在此間隔受控系統內之500組系統參數進行數
	位化結合數位控制器之數位系統之頻率響應封包圖....68
 
表目錄
表3.1	研究比較原始NM及其各種改良型NM的成功率之性能比較23
表3.2	原始NM及其各種改良型NM的平均演化代數之性能比較..24
表4.1	18個測驗函數之格式表............................34
表4.2	演算法控制參數之選取............................35
表4.3    NM、PSO、GA、NM-PSO及NM-PSO-C針對18個測試函數之性 
         能比較..........................................38
表4.4	各種最佳化方法之列表............................39
表4.5	各種最佳化方法的平均函數評估次數之性能比較......39
表5.1	Extremal GM/PMs of the redesigned digital system 
         associated with various digital controllers.....62
表5.2	Extremal GM/PMs of the redesigned digital system 
         associated with various digital controllers.....64

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