平方和模糊系統觀測器設計 -齊次多項式法

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：42

、訪客IP：3.147.68.159

姓名

章為盛(Wei-sheng Chang) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

平方和模糊系統觀測器設計 -齊次多項式法
(SOS-Based Fuzzy Observer Dsigns -Homogeneous Polynomial Approach)

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)

本論文主要研究連續及離散模糊觀測系統的非二次穩定
(Non-quadratic stability) 條件，關於擴展狀態決定於非二次李亞普諾
夫函數，其函數形式是V(e)=1/2e^TQ(e)e，其中條件Q(e)> 0 取決於Q(e)
是一正定的梯度向量(gradient vector)。遺憾的是，此梯度向量Q(e)
是一非凸面體(nonconvex) 的問題，因此可觀測的模糊系統
之穩定性檢測條件，需要使用尤拉齊次多項式定理，並使用其定理之
齊次性質，以平方和方法(Sum of squares) 去檢驗非凸面體問題，使
得其模擬系統之空間解更佳。最後，模擬其多項式模糊系統，表現出
本論文提出之方法是有效的。

摘要(英)

In this thesis, we extend of the state dependent Riccati inequalities to non-quadratic Lyapunov function of the form V (e) = 1/2e^TQ(e)e where Q(e) > 0 requires that Q(e) is a gradient of positive definite function.Unfortunately, the test of Q(e) is nonconvex problem. Thus this thesis studies stabilization problems of the polynomial fuzzy systems via homogeneous Lyapunov functions exploiting the Euler’s homogeneity property to construct a family of SOS polynomials that solves the nonconvexity problem and releases conservatism as well. Lastly, examples of polynomial fuzzy systems are demonstrated to show the proposed
method being effective and effective.

關鍵字(中)

★ 非二次穩定
★ 平方和
★ 參數相依齊次多項式
★ 模糊系統
★ 尤拉齊次多項式定理

關鍵字(英)

★ Non-quadratic stability
★ Sum of squares
★ Homogeneous polynomially parameter-dependent (HPPD) functions
★ T-S fuzzy systems
★ Euler’s Theorem for Homogeneous Functions

論文目次

中文摘要................................................... i
英文摘要.................................................. ii
謝誌 ................................................... iii
目錄 .................................................... iv
圖目錄 ................................................. vi
一、簡介.................................................. 1
1.1 文獻回顧 . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機 . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 論文結構 . . . . . . .. . . . . . . . . . . . . . . . . 3
1.4 符號標記 . . . . . . . . . . . . . . . . . . . . . . . 3
1.5 預備定理 . . . . . . . . . . . . . . . . . . . . . . . 5
二、連續及離散系統架構與檢測條件............................. 7
2.1 連續系統架構 . . . . . . . . . . . . . . . . . . . . . 7
2.2 連續模糊系統之檢測條件（一） . . . . . . . . . . . 9
2.3 尤拉齊次多項式定理 . . . . . . . . . . . . . . . . . 12
2.4 連續模糊系統之檢測條件（二） . . . . . . . . . . . 13
2.5 離散系統架構 . . . . . . . . . . . . . . . . . . . . . 17
2.6 離散模糊系統之檢測條件 . . . . . . . . . . . . . . . 19
三、平方和檢測條件........................................ 23
3.1 平方和檢測法 . . . . . . . . . . . . . . . . . . . . . 23
3.2 連續系統平方和檢測條件 . . . . . . . . . . . . . . . 24
3.3 離散系統平方和檢測條件 . . . . . . . . . . . . . . . 25
四、電腦模擬............................................. 27
4.1 模擬題目（一） . . . . . . . . . . . . . . . . . . . . 27
4.2 模擬題目（二） . . . . . . . . . . . . . . . . . . . . 38
4.3 模擬題目（三） . . . . . . . . . . . . . . . . . . . . 48
4.4 模擬題目（四） . . . . . . . . . . . . . . . . . . . . 51
4.5 模擬題目（五） . . . . . . . . . . . . . . . . . . . . 54
4.6 模擬題目（六） . . . . . . . . . . . . . . . . . . . . 57
五、結論與未來方向........................................ 60
5.1 結論 . . . . . . . . . . . . . . . . . . . . . . . . 60
5.2 未來研究方向 . . . . . . . . . . . . . . . . . . . . . 61
附錄一 .................................................. 62
A.1 波雅定理 . . . . . . . . . . . . . . . . . . . . . . 62
參考文獻................................................. 63

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., 15(1):116–132, January 1985.
[2] M. Sugeno and G.T. Kang. Structure identification of fuzzy model.Fuzzy Set and Systems, 28:15–33, 1988.
[3] K. Tanaka and M. Sugeno. Stability analysis and design of fuzzy control systems. Fuzzy Set and Systems, 45:135–156, 1992.
[4] W.M. Haddad and D.S. Bernstein. Explicit construction of
quadratic Lyapunov functions for the small gain, positive, circle and Popov theorems and their application to robust stability. Part II: discrete-time theory. Int’l J. of Robust and Nonlinear Control,4:249–265, 1994.
[5] P.A. Parrilo. Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization. PhD thesis, Caltech, Pasadena, CA., May 2000.
[6] S. Prajna, A. Papachristodoulou, and P. Parrilo. Introducing SOSTOOLS:a general purpose sum of squares programming solver. In Proc of IEEE CDC, pages 741–746, Montreal, Ca, July 2002.
[7] S. Prajna, A. Papachristodoulou, and et al. New developments on sum of squares optimization and SOSTOOLS. In Proc. the 2004 American Control Conference, pages 5606–5611, 2004.
[8] A. Sala and C. Arino. Polynomial fuzzy models for nonlinear control:
A Taylor series approach. IEEE Trans. Fuzzy Systems, 17(6):
1284–1295, December 2009.
[9] H. Ichihara. Observer design for polynomial systems using convex optimization. In Proc. of the 46th IEEE CDC, pages 5347–5352,New Orleans, LA, December 2007.
[10] J. Xu, K.Y. Lum, and et al. A SOS-based approach to residual generators for discrete-time polynomial nonlinear systems. In Proc.of the 46th IEEE CDC, pages 372–377, New Orleans, LA, December 2007.
[11] J. Xie, L. Xie, and Y. Wang. Synthesis of discrete-time nonlinear systems: A SOS approach. In Proc. of the 2007 American Control Conference, pages 4829–4834, New York, NY, July 2007.
[12] K. Tanaka, H. Yoshida, and et al. A sum of squares approach to stability analysis of polynomial fuzzy systems. In Proc. of the 2007 American Control Conference, pages 4071–4076, New York, NY,July 2007.
[13] K. Tanaka, H. Yoshida, and et al. Stabilization of polynomial fuzzy systems via a sum of squares approach. In Proc. of the 22nd Int’l Symposium on Intelligent Control Part of IEEE Multi-conference on Systems and Control, pages 160–165, Singapore, October 2007.
[14] H. Ichihara and E. Nobuyama. A computational approach to state feedback synthesis for nonlinear systems based on matrix sum of squares relaxations. In Proc. 17th Int’l Symposium on Mathematical Theory of Network and Systems, pages 932–937, Kyoto, Japan,2006.
[15] C.W.J. Hol and C.W. Scherer. Sum of squares relaxations for polynomial semidefinite programming. In Proc.of MTNS, pages 1–10,2004.
[16] E. Kim and H. Lee. New approaches to relaxed quadratic stability condition of fuzzy control systems. IEEE Trans. Fuzzy Systems,8(5):523–534, October 2000.
[17] X.D. Liu and Q.L. Zhang. New approaches to H1 controller designs based on fuzzy observers for T-S fuzzy systems via LMI. Automatica,39:1571–1582, June 2003.
[18] C.H. Fang, Y.S. Liu, S.W. Kau, L. Hong, and C.H. Lee. A new LMI-based approach to relaxed quadratic stabilization of T-S fuzzy control systems. IEEE Trans. Fuzzy Systems, 14(3):386–397, June 2006.
[19] M. Johansson, A. Rantzer, and K.-E. Arzen. Piecewise quadratic stability of fuzzy systems. IEEE Trans. Fuzzy Systems, 7(6):713–722, December 1999.
[20] G. Feng. Controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions. IEEE Trans. Circuits and Syst. I:Fundamental Theory and Applications, 11(5):605–612, 2003.
[21] D. Sun G. Feng, C. Chen and Y. Zhu. H1 controller synthesis of fuzzy dynamic systems based on piecewise Lyapunov functions and bilinear matrix inequalities. IEEE Trans. Circuits and Syst. I:Fundamental Theory and Applications, 13(1):94–103, 2005.
[22] T. M. Guerra and L. Vermeiren. LMI-based relaxed nonquadratic stabilization conditions for nonlinear systems in the Takagi-Sugeno’s form. Automatica, 40:823–829, 2004.
[23] B.C. Ding, H. Sun, and P Yang. Further studies on LMI-based relaxed stabilization conditions for nonlinear systems in Takagisugeno’s form. Automatica, 43:503–508, 2006.
[24] X. Chang and G. Yang. FA descriptor representation approach to observer-based H∞ control synthesis for discrete-time fuzzy systems.Fuzzy Set and Systems, 185(1):38–51, 2010.
[25] B. Ding. Stabilization of Takagi-Sugeno model via nonparallel distributed compensation law. IEEE Trans. Fuzzy Systems, 18(1):188–194, February 2010.
[26] A. Jaadari J. Pan, S. Fei and T. M. Guerra. Nonquadratic stabilization of continuous T-S fuzzy models: LMI solution for local approach. IEEE Trans. Fuzzy Systems, 20(3):594–602, 2012.
[27] J. B. Park D. H. Lee and Y. H. Joo. Approaches to extended non-quadratic stability and stabilization conditions for discrete-time Takagi-Sugeno fuzzy systems. Automatica, 47(3):534–538, 2011.
[28] Kazuo Tanaka, Hiroshi Ohtake, Toshiaki Seo, Motoyasu Tanaka,and Hua O Wang. Polynomial fuzzy observer designs: a sum-ofsquares approach. Systems, Man, and Cybernetics, Part B: Cybernetics,IEEE Transactions on, 42(5):1330–1342, 2012.
[29] K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang. A sum of squares approach to modeling and control of nonlinear dynamical systems with polynomial fuzzy systems. IEEE Trans. Fuzzy Systems,17(4):911–922, August 2009.
[30] C. Ebenbauer, J. Renz, and F. Allgower. Polynomial Feedback and Observer Design using Nonquadratic Lyapunov Functions.
[31] S. Prajna, A. Papachristodoulou, and F. Wu. Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based Approach.In Proc. 5th Asian Control Conference, pages 157–165, July
2004.
[32] V. Power and B. Reznick. A new bound for Pólya’s Theorem with applications to polynomials positive on polyhedra. J. Pure Appl.Algebra, 164:221–229, 2001.
[33] J. de Loera and F. Santos. An effect version of Pólya’s Theorem onpositive definite forms. J. Pure Appl. Algebra, 108:231–240, 1996.

指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2014-7-28

推文