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研究生:陳巧雯
研究生(外文):Chiao-Wen Chen
論文名稱:有效保結構的冪法求解廣義連續型及離散型黎卡迪方程
論文名稱(外文):Generalized Structure-Preserving Doubling Algorithms for Generalized Continuous and Discrete Time Algebraic Riccati Equations
指導教授:林文偉林文偉引用關係
指導教授(外文):Wen-Wei Lin
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學門:數學及統計學門
學類:數學學類
論文種類:學術論文
論文出版年:2005
畢業學年度:93
語文別:英文
論文頁數:36
中文關鍵詞:黎卡迪方程
外文關鍵詞:the Caley transformationgeneralized continuous-time algebraic Riccati equationgeneralized discrete-time algebraic Riccati equationstructure-preserving doubling algrithm
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本論文主要是以可轉換連續型與散型控制系統的凱利變換為基礎,運用並根據保結構法(SDA)的概念,發展一套G-SDA法,來求解廣義連續型及離散型的黎卡迪方程。文中依各類型,分別列舉在矩陣E條件數偌大的情況下,本法的數值結果,以說明G-SDA法的有效性與特色。
In this paper we extend the structure-preserving doubling algorithm (SDA) to compute the symmetric positive semi-definite solutions of the generalized continuous as well as discrete algebraic Riccati equations. Our main idea is to relate continuous and discrete time control systems based on the generalized Caley transformation.
In the end, we select some examples to illustrate that the G-SDA performs better than the MATLAB commands in the control toolbox.
1 Introduction...1
1.1 Generalized Continuous-Time Algebraic Riccati Equations
1.2 Generalized Discrete-Time Algebraic Riccati Equaitons
2 G-SDA Algorithm for G-CAREs...6
3 G-SDA Algorithm for G-DAREs...10
4 Convergence of G-SDA Algorithm...18
5 Numerical Experiments for G-CAREs...20
6 Numerical Experiments for G-DAREs...28
7 Conclusions...32
[1] E. K.-W. Chu, H. Y. Fan, W. W. Lin, and C.-S.Wang (2004). A Structure-Preserving
Algorithm for Periodic Discrete-Time Algebraic Riccati Equations, Int. J. Control,
Vol. 77, no. 8, pp. 767-788.
[2] E. K.-W. Chu, H. Y. Fan, and W. W. Lin (2005). A Structure-Preserving Doubling
Algorithm for Continuous-Time Algebraic Riccati Equations, Lin. Alg. Appl., Vol.
396, pp. 50-80.
[3] E. K.-W. Chu, H. Y. Fan, and W. W. Lin (2003). A Generalized Structure-Preserving
Doubling Algorithm for Generalized Discrete-Time Algebraic Riccati Equations,
preprint 2002-29, NCTS, National Tsing Hua University, Hsinchu 300, Taiwan.
[4] V. L. Mehrmann (1991). The Autonomous Linear Quadratic Control Problem: Theory
and Numerical Solution, Berlin, Springer-Verlag.
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09107 Chemnitz, FRG.
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Hsinchu 300, Taiwan.
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Johns Hopkins University Press.
[8] K. Zhou, J. C. Doyle, and K. Glover (1996). Robust and Optimal Control, New Jersey,
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[9] M. S. Bazaraa, H. D. Sherali, and C. M. Shetty (1993). Nonlinear Programming:
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http://www.tu-chemnitz.de/sfb393/spc95pr.html.
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