本文提出ㄧ種改良式非同步(asynchronous)並行處理(parallel computation)之粒子群聚最佳化法(particle swarm optimization, PSO)，以提升粒子群聚最佳化法在異質(heterogynous)的計算環境中之計算效率。作法上係綜合傳統的同步化(synchronous)與非同步化(asynchronous)並行處理計算法，以僕工作端(slave)之性能為基準，分配適當的粒子數量，實驗結果證實我們所提出的方法具有良好之性能，可以提升粒子群聚最佳化法之計算效能。
    第二部份係以PSO為基礎，探討不確定間隔系統之數位化再設計，作法上主要係以時間響應作為比較之基礎，針對連續時間間隔系統最好與最差情況下系統響應之信號能量(Best-case and worst-case signal energy)與數位化再設計後數位系統最好與最差情況下系統響應之序列能量(sequence energy)的差異作評估，並且將此問題規劃表示成ㄧ最佳化的問題，再利用PSO來求解。設計的目標是求得一最佳數位化再設計控制器(optimal redesigned digital controller)，使得數位化系統之最好與最差的系統響應很接近於連續時間系統最好與最差的系統響應。
    第三部份則以PSO為基礎，針對以狀態空間表示之連續時間系統做數位化再設計，作法上係以數位化再設計系統與原始連續時間系統之狀態的差異作為評估的機制，利用PSO設計以求得一最佳數位控制法則，使得數位化再設計系統之狀態能夠近似原始連續時間系統之狀態。

An enhanced asynchronous parallel computation scheme for particle swarm optimization (PSO) is proposed in this paper to improve computational efficiency for heterogeneous workstations. Taking advantages of the conventional parallel computation methods of synchronous and asynchronous approaches, the proposed method distributes appropriate number of particles to slave workstations depending on performance of the individual workstations. Simulation results indicate that the proposed method has a good computational performance, with a significant improvement on the computation efficiency.    
The second part of this thesis is a novel design approach of a digital controller based on time-response resemblance of the closed-loop system via particle swarm optimization to improve performance of the redesigned digital system for continuous-time uncertain interval systems. The design rationale of the proposed approach is to derive a digital controller for the redesigned digital system so that step response sequences corresponding to the extremal sequence energy closely match those of their continuous counterpart under the perturbation of the plant parameters. By suitably formulating the design problem as an optimization problem, and subsequently solved via PSO, a set of optimal parameters for the digital controller subject to time responses of the redesigned digital system having an interval plant can be derived, providing. 
The third part is regarding digital redesign of continuous-time system described in state space representation via particle swarm optimization. The design objective is to determine an optimal digital control law, which allows the states of the digitally controlled system to closely match those of the original analog system.

目錄
中文摘要.........................................................................................................I
英文摘要.......................................................................................................III
致謝.................................................................................................................V
目錄................................................................................................................VI
圖目錄........................................................................................................IX
表目錄...........................................................................................................XI
第一章 緒論..................................................................................................1
第二章 粒子群聚最佳化法(PSO)............................................................6
第三章 以並行處理為基礎之粒子群聚最佳化法.............................9
3.1 建立並行處理架構..................................................................................10
3.2 傳統並行處理方法介紹..........................................................................13
3.2.1 同步化並行處理...........................................................................13
3.2.2 非同步化並行處理.......................................................................14
3.3 傳統並行處理方法之優缺點..................................................................14
3.4 改良式非同步並行處理之粒子群聚最佳化法......................................15
3.5 改良式並行處理PSO之應用...................................................................18
3.5.1 Minimax最佳化問題......................................................................18
3.5.2 系統模型降階問題.......................................................................19
3.6 並行處理環境..........................................................................................20
3.7 範例..........................................................................................................21
第四章 以PSO為基礎之不確定間隔系統之數位化再設計..........27
4.1 問題描述..................................................................................................27
4.2 數位化再設計系統之性能評估..............................................................31
4.2.1 連續時間信號能量(CSE)..............................................................32
4.2.2 離散時間序列能量(DSE).............................................................33
4.2.3 間隔系統積分平方誤差(ISE)之極值情況.................................34
4.2.4 數位化再設計系統誤差序列能量(ESE)之極值情況.................35
4.3 以PSO為基礎之最佳數位控制器設計...................................................37
4.3.1 PSO2和PSO3適應函數之評估機制..............................................40
4.3.2 PSO1適應函數之評估機制...........................................................41
4.4 範例..........................................................................................................42
第五章 以PSO為基礎之確定系統以狀態空間表示之數位化再設計..…..................…................................................................…52
5.1 問題描述..................................................................................................53
5.2 以PSO為基礎之最佳數位控制法則設計...............................................55
5.3 範例..........................................................................................................56
第六章 結論與未來研究方向................................................................64
6.1 結論..........................................................................................................64
6.2 未來研究方向..........................................................................................65
參考文獻.......................................................................................................66
研究著作.......................................................................................................73












圖目錄
圖2.1 模擬鳥或魚群的群聚模式………….………………………………7
圖2.2 粒子群聚最佳化法流程圖……….…………………………………8
圖3.1 以並行處理為基礎之PSO演算法架構圖…………………………..12
圖3.2 同步PSO並行處理概念圖…………….……………..…………….13
圖3.3 非同步PSO並行處理概念圖………..……………………………..14
圖3.4 以主從計算架構進行之非同步並行處理PSO之演化方塊圖……17
圖3.5 以PSO為基礎求解minimax問題之架構…………...…...………...18
圖3.6 以PSO調整之系統降階模型方塊圖……………………………….20
圖3.7 範例2synchronous與asynchronous所模擬出的步級響應圖……..25
圖3.8 範例2改良式PSO並行處理與單台電腦所模擬之步級響應圖........26
圖4.1 具有間隔受控體之連續時間控制系統…..………….…………….28
圖4.2 數位化再設計系統……………………………….………………..29
圖4.3 以PSO為基礎解決數位化再設計問題之流程圖……….…………38
圖4.4 利用三個PSO處理數位化再設計問題之架構……………………40
圖4.5 範例1中連續時間最好與最差之時間響應……………………….43
圖4.6 範例1中利用PSO演化搜尋和Tustin轉換所求得之數位控制器之最好離散時間步級響應與原類比系統之最好步級響應…………..45
圖4.7 範例1中利用PSO演化搜尋和Tustin轉換所求得之數位控制器之最差離散時間步級響應與原類比系統之最差步級響應..…….…..46
圖4.8 範例2中連續時間最好與最差之時間響應………….…….……….48
圖4.9 範例2中利用PSO演化搜尋和Tustin轉換所求得之數位控制器之最好離散時間步級響應與原類比系統之最好步級響應…….……50
圖4.10 範例2中利用PSO演化搜尋和Tustin轉換所求得之數位控制器之最差離散時間步級響應與原類比系統之最差步級響應片……….51
圖5.1 利用PSO解決針對狀態空間表示之數位化再設計方塊圖…….…..55
圖5.2 範例1之原始連續時間系統狀態xc(t)……………………....……..57
圖5.3 範例1之原始連續時間系統狀態與PSO為基礎之數位化再設計之系統狀態……………....…………….………..…………..…………59
圖5.4 範例1之原始連續時間系統狀態與Pade為基礎之數位化再設計之系統狀態…………………………………………………………….60
圖5.5 範例1之原始連續時間系統狀態與Bilinear為基礎之數位化再設計之系統狀態……..…….…………………………………………..61
圖5.6 範例1之原始連續時間系統狀態與Improved block-pulse為基礎之數位化再設計之系統狀態…….………………………..…………..62

表目錄
表3.1 slave端之電腦規格……………..………….…….…………………20
表3.2 測試運算式之執行時間…………………….………….……….…21
表3.3 群組粒子分配結果………..….…………………..…….……………21
表3.4 minimax最佳化問題之實驗結果………….……….………………22
表3.5 利用四種方法求解之結果……….…………….…….……………23
表3.6 系統模型降階實驗結果………….…………….……….…………24
表4.1 範例1中三個PSO所使用之參數…………...……………...………44
表4.2 範例1所提出之方法和傳統數位化方法與原類比系統相似度比較47
表4.3 範例2中三個PSO所使用之參數……..…….………………………49
表4.4 範例2所提出之方法和傳統數位化方法與原類比系統相似度比較51
表5.1 四種數位化再設計方法與連續時間系統之精確度比較…………63

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