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論文名稱 Title |
一種以分散式計算提升計算效率之強韌性分析方法 A Computationally Efficient Method for Robustness Analysis based on Distributed Computation |
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系所名稱 Department |
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畢業學年期 Year, semester |
語文別 Language |
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學位類別 Degree |
頁數 Number of pages |
65 |
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研究生 Author |
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指導教授 Advisor |
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召集委員 Convenor |
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口試委員 Advisory Committee |
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口試日期 Date of Exam |
2017-07-24 |
繳交日期 Date of Submission |
2017-09-16 |
關鍵字 Keywords |
強韌穩定性、分散式運算、KYP引理、二次積分限制、(凸型)最佳化 integral quadratic constraint, robust stability, Distributed computing, convex feasibility problem, KYP lemma |
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統計 Statistics |
本論文已被瀏覽 5674 次,被下載 24 次 The thesis/dissertation has been browsed 5674 times, has been downloaded 24 times. |
中文摘要 |
許多檢測系統強韌穩定性的方法,乃是將強韌穩定性檢測問題,約化為一(凸型)最佳化的可行性求解問題。在這類方法中,以「二次積分限制」分析方法最具代表性;許多強韌穩定性判別法則,都可視為「二次積分限制」分析方法的應用。在分析具許多子系統的大型網路系統的情況下,應用「二次積分限制方法」所衍生的可行性求解問題會有許多變數需要求解,限制條件的維度也會很大。求解這類問題需要巨大的計算資源;若以單一電腦來求解這類問題,運算時間將會很長且記憶體有可能會不足。 本研究延續文獻[1]的方法,提出一分解「二次積分限制方法」所衍生的大型可行性求解問題成諸多「小維度」問題,且能將「小維度」問題分給多台電腦並行運算求解的方法。吾人所提一之分解方法與[1]相同,但改進了求解「小維度」問題的做法。我們應用KYP引理,並利用文獻[17]中提議的演算法,來改良數值解的精準度及分散式運算的收斂速率。比較文獻[1],吾人所提議的方法在「小維度」問題的狀態變數較少時,在運算效率上具有相當大的優勢。隨機產生的數值實驗結果也印證了這個趨勢。 |
Abstract |
A common and important feature amongst the "modern" robustness analysis approaches is that the analysis problem is transformed into a (convex) feasibility problem, and the existence of a feasible solution implies that the system under consideration does possess the robustness property we desire. The Integral Quadratic Constraint (IQC) analysis is a well-known representative of such approaches; as a matter of fact, many robustness criteria can be obtained via applying IQC analysis. Applying the IQC analysis to analyze a large scale complex network which has many subsystems would usually result in a feasibility problem with many (hundreds of thousands) decision variables as well as many high-dimensional constraints. Solving such problems usually require gigantic computational resources. In particular, solving such problems in a centralized fashion using a single computer would usually take a very long time and most likely run out of memory space before finding a solution. In this thesis, we follow the methodology proposed in [1] and propose a methodology and algorithm for decomposing a large scale (in terms of the number of decision variables and the state space dimension) IQC problem into many small scale problems, and distributing these small problems to many computers to solve them in a distributed fashion. Our methodology for decomposing the large scale problem is the same as that proposed in [1]; however, our algorithm for solving the small scale problems are different from [1]. An improvement for finding more accurate feasible solutions in a fast-convergent fashion is proposed, by applying KYP lemma and the algorithms proposed in [17]. Compared to [1], our approach has a decisive advantage in the case where the small scale problems have a small number of decision variables with a small dimension state-space system. In such cases, our approach is computationally much more efficient. The results of randomly generated numerical experiments confirm this fact. |
目次 Table of Contents |
[緒論+1] [文獻回顧 +1] [強韌控制與二次積分限制分析理論 +1] [分散地分析相互連接的不確定系統 +2] [凸面可行性問題與分散的演算法 +3] [研究動機、目的與貢獻 +4] [符號說明 +5] [預備知識 +8] [IQC 定理 +8] [Kalman-Yakubovich-Popov 引理 +9] [圖論 +10] [問題的描述與分解 +17] [問題的描述 +17] [為什麼要分解問題? +17] [問題的分解 +18] [Sina Khoshfetrat Pakazad的方法 +23] [我們的方法 +31] [零散成組的可行性問題與分散演算法 +37] [凸面可行性問題 +37] [誤差邊界與有界線性一致性+37] [乘法空間形式+38] [凸面最小化形式+39] [近似操作子與近似分裂法+39] [向前向後分裂法+40] [分散解法+42] [近似分裂法與分散應用+42] [局部收斂測試+44] [收斂速率+46] [可行問題+46] [不可行問題+47] [數值結果+48] [隨機例子的資料+48] [隨機例子中積分不等式的乘數+48] [隨機例子中的轉移函數矩陣的結構+48] [隨機例子中的轉移函數矩陣的結構+48] [可行的問題+50] [記憶體不足+50] [結論與未來展望+51] [結論+51] [未來展望+51] [參考文獻+52] |
參考文獻 References |
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