耗散性估測器-波雅定理

以作者查詢圖書館館藏

、以作者查詢臺灣博碩士

、以作者查詢全國書目

、勘誤回報

、線上人數：28

、訪客IP：3.140.185.123

姓名

吳東陵(Dong-Lin Wu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

耗散性估測器-波雅定理
(Dissipative Filtering-Polya's theorem)

相關論文

★ 強健性扇形區域穩定範圍之比較	★ 模糊系統混模強健控制
★ T-S模糊模型之建構、強健穩定分析與H2/H∞控制	★ 廣義H2模糊控制-連續系統線性分式轉換法
★ 廣義模糊控制-離散系統線性分式轉換法	★ H∞模糊控制－連續系統線性分式轉換法
★ H∞模糊控制—離散系統線性分式轉換法	★ 強健模糊動態輸出回饋控制-Circle 與 Popov 定理
★ 強健模糊觀測狀態回饋控制-Circle與Popov定理	★ H_infinity 取樣模糊系統的觀測型控制
★ H∞取樣模糊系統控制與觀測定理	★ H-ihfinity取樣模糊系統動態輸出回饋控制
★ H∞模糊系統控制-多凸面法	★ H∞模糊系統控制-寬鬆變數法
★ 時間延遲 T-S 模糊系統之強健 H2/H(Infinity) 控制與估測	★ 寬鬆耗散性模糊控制-波雅定理

檔案

[Endnote RIS 格式]

[Bibtex 格式]

[相關文章]

[文章引用]

[完整記錄]

[館藏目錄]

[檢視]

[下載]

本電子論文使用權限為同意立即開放。
已達開放權限電子全文僅授權使用者為學術研究之目的，進行個人非營利性質之檢索、閱讀、列印。
請遵守中華民國著作權法之相關規定，切勿任意重製、散佈、改作、轉貼、播送，以免觸法。

摘要(中)

本論文是研究模糊系統 (fuzzy systems)所代表的非線性系統之估測問題,並且藉由耗散性的探討,來描述一廣義之性能指標 ,以及應用波雅定理 (Pólya’s theorem)於檢測條件上 ,來得到一較為寬鬆的檢測條件。內容方面本論文將分為兩部分來進行討論 ,第一部份先推導滿足耗散性的檢測條件,第二部分代入波雅定理的概念 ,來加以求解第一部分的 LMIs。
本論文將在 LMI(LinearMatrixInequality)中探討一個新的降低保守性的檢測條件,連續及離散模糊系統將由統一的方法來論述。藉由建立在李亞普諾夫函數 (Lyapunov function)及參數相依齊次多項式-LMIs(HomogeneousPolynomialParameterDependent-LMIs)解之結構的概念 ,可設計一高次齊次多項式矩陣解滿足 LMI,即待求的估測器增益不必為一次式 ,而可以是一高次齊次式增益,來加以估測,在求解檢測條件方面,代入波雅定理,降低檢測條件的保守性,以求得較佳的解。
本論文同時也研究估測一非線性系統之某些狀態並滿足所要求的性能,首先將此非線性系統以 Takagi-Sugeno(T-S)模糊系統來描述之,以提供一套系統化的研究方法 ,研究非線性系統與估測系統所組成的估測誤差系統的穩定性與性能的分析問題。針對 T-S模糊模型,本論文根據 HPPD-LMI的概念設計一高次齊次多項式矩陣估測器,並探討估測誤差系統是否滿足耗散性,最後代入波雅定理探討求解的檢測條件,進而達到共同 P二次李亞普諾夫穩定的充要條件。

摘要(英)

A new stabilization condition guaranteeing dissipativity of T-S fuzzy filtering error systems is studied in this paper,
continuous- and discrete-time fuzzy filtering error systems treated in a unified manner.
A premise-dependent HPPD gain (i.e., grade of membership, μ) is considered.
The stabilization and performance analysis is performed on the basis of dissipativity,
here stated using LMI to profit from the advantage of convex optimization.
Using Pólya’’s theorem, we can see the reduction of conservative, such that the performance get more and more better.
It is shown, via theoretical analysis and numerical simulations, that our results are much
less conservative via Pólya’’s theorem.

關鍵字(中)

★ 波雅定理
★ 耗散性
★ 估測器

關鍵字(英)

★ Polya's theorem
★ dissipative
★ filter

論文目次

目錄
論文摘要 I
誌謝 IV
圖目 VIII
第一章簡介 1
1.1文獻回顧 ························· 1
1.2研究動機 ························· 3
1.3論文結構 ························· 3
1.4符號標記 ························· 4
1.5預備定理 ························· 4
第二章系統數學模型 6
2.1系統的數學模型 ····················· 6
2.2估測器的數學模型 ···················· 7
2.2.1 Case A :獨立於估測的狀態變數 ··········· 8
2.2.2 Case B :相依於估測的狀態變數 ··········· 13
第三章耗散性–估測器 15
3.1耗散性定義 ······················· 15
3.2 CaseA :獨立於估測的狀態變數 ············ 18
3.2.1連續系統 ······················· 18
3.2.2離散系統 ······················· 22
3.3 CaseB :相依於估測的狀態變數 ············ 24
3.3.1連續系統 ······················· 24
3.3.2離散系統 ······················· 27
第四章電腦模擬 30
4.1 Case A連續例子 ···················· 30
4.1.1估測器設計與求解-連續系統(CaseA) ········ 33
4.2 Case B離散例子 ···················· 38
4.2.1估測器設計與求解-離散系統 (Case B) ······· 39
第五章波雅定理之應用 45
5.1波雅定理 ························· 46
5.2 CaseA :獨立於估測的狀態變數 ············ 48
5.2.1連續系統 ······················· 48
5.2.2離散系統 ······················· 51
5.3 CaseB :相依於估測的狀態變數 ············ 53
5.3.1連續系統 ······················· 53
5.3.2離散系統 ······················· 55
第六章電腦模擬 58
6.1 Case A離散例子 ···················· 58
6.1.1估測器設計與求解-離散系統(CaseA)········· 59
6.2 Case B離散例子 ···················· 60
6.2.1估測器求解-離散系統 (Case B) ············ 60
第七章結論與未來發展 62
7.1總結 ··························· 62
7.2未來研究 ························· 63
參考文獻 64

參考文獻

參考文獻
[1] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modelling and control,” IEEE Trans. Syst., Man, Cybern., vol. 15, no. 1, pp.
116–132, Jan. 1985.
[2] K. Tanaka and H. Wang, Fuzzy Control Systems Design: A Linear Matrix Inequality Approach. New York, NY: John Wiley & Sons, Inc., 2001.
[3] H.Ying, “Sufficient conditionsonuniformapproximationof multivariatefunctions
by Takagi-Sugeno fuzzy systems with linear rule consequent,” IEEE Trans. Syst., Man, Cybern. A: Systems and Humans, vol. 28, no. 4, pp. 515–520, Apr. 1998.
[4] H. Wang, J. Li, D. Niemann, and K. Tanaka, “T-S fuzzy model with linear rule consequence and PDC controller: a universal framework for nonlinear control systems,” in Proc. of 18th Int’l Conf. of the North American Fuzzy Information Processing Society, 2000.
[5] K. Tanaka, T. Taniguchi, and H. Wang, “Generalized Takagi-Sugeno fuzzy systems: rule reduction and robust control,” in Proc. of 7th IEEE Conf. on Fuzzy
Systems, 2000.
[6] T. Taniguchi, K. Tanaka, H. Ohatake, and H. Wang, “Model construction, rule reduction and robust compensation for generalized form of Takagi-Sugeno fuzzy
systems,” IEEE Trans. Fuzzy Systems, vol. 9, no. 4, pp. 525–538, Aug. 2001.
[7] J. C.Lo and M. L.Lin, “Observer-based robust H∞ control for fuzzy systems using two-stepprocedure,” IEEETrans.FuzzySystems, vol.12, no.3,pp.350–359,June
2004.
[8] P. Bliman, “An existence reult of polynmial solutions of parameter-dependent LMIs,” Syst. & Contr. Lett., vol.51, no.3-4,pp.165–169,2004.
[9] P. A. Bliman, R. C. L. F. Oliveira, V. F. Montagner, and P. L. D. Peres, “Existence of homogeneous polynomial solutions for parameter-dependentlinear matrix inequalities with parameters in the simplex,” in Proc. of 45th IEEE Conf. on Deci and Contr, Dec. 2006, pp. 1486–1491.
[10] R. C. L. F. Oliveira and P. L. D. Peres, “LMI conditions for robust stability analysis based on polynomially parameter-dependent Lyapunov functions,” Syst. & Contr. Lett., vol. 55, pp. 52–61, 2006.
[11] Z. Tan, Y. Soh, and L.Xie, “Dissipative control for linear discrete-time systems,” Automatica, vol. 35, pp. 1557–1564, 1999.
[12] J.Willems, “Dissipative dynamical systems Part1:General theory,” Arch. Rational Mech. Analy., vol. 45, pp. 321–351, 1972.
[13] ——, “Dissipativedynamical systems-Part2:Linear systems with quadratic supply rates,” Arch. Rational Mech. Analy., vol. 45, pp. 352–393, 1972.
[14] S. Xie, L. Xie, and C. E. De Souza, “Robust dissipative control for linear systems with dissipative uncertainty,” Int. J. Contr., vol. 70, no. 2, pp. 169–191, 1998.
[15] S.Yuliar,M.R.James,andJ.W.Helton, “Dissipative Control Systems Synthesis with Full State Feedback,” Nov. 1995.
[16] C. Tseng, “Robust fuzzy filter desing for nonlinear systems with persistent bounded disturbance,” IEEE Trans. Syst., Man, Cybern. B: Cybernetics, vol. 36, no. 4, pp. 940–945, Aug. 2006.
[17] Y. C. Lin and J. C. Lo, “Robust mixed H2/H∞ filtering for time-delay fuzzy systems,” IEEE Trans. Signal Processing, vol. 54, no. 8, pp. 2897–2909, Aug.
2006.
[18] ——, “Robust mixed H2/H∞ filtering for discrete-time delay fuzzy systems,” Int’l J. of Systems Science, vol. 36, no. 15, pp. 993–1006, Dec. 2005.
[19] S.K.Nguang,W.Assawinchaichote,P.Shi,andY.Shi, “H∞ fuzzy filter design for uncertain nonlinear systems with Markovian jumps:An LMI approach,” American Control, 2005.
[20] S. Zhou, J. Lam, and A. Xue, “H∞ filtering of discrete-time fuzzy systems via basis-dependent Lyapunov function approach,” Fuzzy Sets and Systems,pp. 180– 193, 2007.
[21] Y.C.LinandJ.C.Lo, “Exponential stability of filtering problems for delay fuzzy systems,” in Proc. 2004 IEEE Int’l Conf.Networking, Sensing and Control, vol.2, Taipei, TW, Mar. 2004, pp. 926–931.
[22] ——, “H∞ filter/control design for discrete-time Takagi-Sugeno fuzzy systems with time delays,” in Proc. 2004 Conf. Asia Contr., vol. 1, Melbourne, AU, Dec. 2004.
[23] E.FridmanandU.Shaked, “A new H∞ filter design for linear time delay systems,” IEEE Trans. Signal Processing, vol. 49, no. 11, pp. 2839–2843, Nov. 2001.
[24] H. Tuan, P. Apkarian, and T. Nguyen, “Robust and reduced-order filtering: new LMI-based characterizations and Methods,” IEEE Trans. Signal Processing, vol. 49, pp. 2975–2984, Dec. 2001.
[25] S.XuandJ.Lam, “Exponential H∞ filter design for Takagi-Sugeno fuzzy systems with time delay,” Engineering Applications of Artificial Intelligence,pp. 645–659, 2004.
[26] R. Martinez Palhares, C. E. de Souza, and P. L. Dias Peres, “Robust H∞ filtering for Uncertain discrete-time state-delay systems,” Engineering Applications of
Artificial Intelligence,pp. 645–659, 2001.
[27] Jan C. Willems and H. L. Trentelman, “Synthesis of Dissipative Systems Using Quadratic Differential Forms : Part I,” IEEE Trans. Automatic Control, vol. 47, no. 1, pp. 53–69, Jan. 2002.
[28] ——, “Synthesis of Dissipative Systems Using Quadratic Differential Forms : Part II,” IEEE Trans. Automatic Control, vol. 47, no. 1, pp. 70–86, Jan. 2002.
[29] W. Assawinchaichote, S. K. Nguang, and P. Shi, “Robust H∞ fuzzy filter design for uncertain nonlinear singularly perturbed systems with Markovian jumps:An
LMI approach,” ELSEVIER,ScienceDirect,InformationScience,2006.
[30] H. Zhang, S. Lun, and D. Liu, “Fuzzy H∞ filter design for class of nonlinear discrete-time systems with multiple time delays,” IEEE Trans. Fuzzy Systems,2007.
[31] Y. Cao and P. Frank, “Analysis and synthesis of nonlinear time-delay systems via fuzzy control approach,” IEEE Trans. Fuzzy Systems, vol. 8, no. 2, pp. 200–211,
Apr. 2000.
[32] V.PowerandB.Reznick, “A new bound for Pólya’s Theorem with applicationsto polynominals positive on polyhedra,”J.PureAppl.Algebra, vol.164,pp.221–229,
2001.
[33] C. W. Scherer, “Relaxations for robust linear matrix inequality problems with verification for exactness,” SIAM J. Matrix Anal.Appl., vol. 27, no. 2, pp. 365– 395, 2005.

指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2008-6-24

推文