博碩士論文 104323111 詳細資訊




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姓名 巴宇平(Yu-Ping Ba)  查詢紙本館藏   畢業系所 機械工程學系
論文名稱 齊次多項式尤拉法應用於切換式模糊觀測器設計
(Piecewise Fuzzy Observer Design - Homogeneous Polynomial Lyapunov Euler Method)
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摘要(中) 本論文主要研究連續模糊系統之非二次穩定(non-quadratic stability)
條件下的片段式李亞普諾夫函數,再加入切換式觀測器去提升
追蹤狀態的效能。藉由改變穩定度條件裡的變數,使數個李亞普諾
夫函數得以交錯,重新組成一片段式李亞普諾夫函數,其中皆以尤拉
齊次多項式定理建立非二次李亞普諾夫函數(non-quadratic Lyapunov
function),其形式為
V (x) = xTP(x)x = 1
g(g??1)xT?xxV (x)x。
然後再使用求得的李亞普諾夫函數之交錯時間點去設計切換式觀
測器,在設計切換式觀測器的過程中,也去探討不同類型的系統(系
統矩陣是否包含待估測狀態),所需的觀測器格式與穩定度條件。
例題模擬部分,先以泰勒級數建模得出模糊系統,且以非二次的
李亞普諾夫函數及對時間的變化率作為穩定的條件,加入片段式結構
後,再以平方和方法(Sum-of-Squares) 來檢驗模糊系統的穩定條件,
並設計出合適的切換式觀測器。
摘要(英) The main contribution in this thesis is Piecewise-Lyapunov-Function-
Based Switching Fuzzy Observer with non-quadratic stability for continuous
fuzzy system. At first, we consider several non-quadratic Lyapunov
function with form designed as
V (x) = xTP(x)x = 1
g(g??1)xT?xxV (x)x.
Then, we combine these Lyapunov functions into one Piecewise-
Lyapunov-Function by the parameter, , and design the Switching Observer
by using the crossing point forming Piecewise-Lyapunov-Function.
At the same time, we investigate the stable condition with different type
fuzzy system.
In numerical simulation, we solve for Piecewise-Lyapunov-Function-
Based Switching Fuzzy Observer with sum-of-squares approach.
關鍵字(中) ★ Takagi-Sugeno 模糊系統
★ 片段式李亞普諾夫函數
★ 切換式觀測器
★ 非二次穩定
★ 平方和
★ 尤拉齊次多項式定理
★ 泰勒級數
關鍵字(英) ★ T-S fuzzy systems
★ Piecewise Lyapunov function
★ Switching observer
★ Non-quadratic stability
★ Sum of squares
★ Euler’s Theorem for Homogeneous Functions
★ Taylor-Series
論文目次 中文摘要 i
英文摘要 ii
謝誌 iii
目錄 iv
圖目錄 vi
1、背景介紹 1
1.1 文獻回顧 1
1.2 研究動機 2
1.3 論文結構 4
1.4 符號標記 4
1.5 預備定理 5
2、系統架構與檢測條件 7
2.1 模糊系統與模糊觀測系統架構 7
2.2 尤拉齊次多項式定理 11
2.3 片段式李亞普諾夫函數 15
2.4 片段式齊次李亞普諾夫函數與切換式模糊觀測器 18
2.5 穩定度條件 20
3、模糊建模方法及平方和檢測法 32
3.1 泰勒級數模糊 32
3.2 平方和檢驗法 35
3.3 平方和檢驗法之片段式齊次李亞諾夫觀測系統 38
4、電腦模擬 43
4.1 例題一 43
4.2 例題二 59
4.3 例題三 74
4.4 例題四 94
5、結論與未來方向 108
5.1 結論 108
5.2 未來研究方向 109
文獻 110
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] M. Sugeno and G. Kang, “Structure identification of fuzzy model,”
Fuzzy Set and Systems, vol. 28, pp. 15–33, 1988.
[3] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy
control systems,” Fuzzy Set and Systems, vol. 45, pp. 135–156,
1992.
[4] W. Haddad and D. Bernstein, “Explicit construction of quadratic
Lyapunov functions for the small gain, positive, circle and Popov
theorems and their application to robust stability. Part II: discretetime
theory,” Int’l J. of Robust and Nonlinear Control, vol. 4, pp.
249–265, 1994.
[5] S. Prajna, A. Papachristodoulou, and P. Parrilo, “Introducing SOSTOOLS:
a general purpose sum of squares programming solver,” in
Proc of IEEE CDC, Montreal, Ca, Jul. 2002, pp. 741–746.
[6] S. Prajna, A. Papachristodoulou, and et al, “New developments on
sum of squares optimization and SOSTOOLS,” in Proc. the 2004
American Control Conference, 2004, pp. 5606–5611.
[7] Kazuo Tanaka, Hiroto Yoshida, Hiroshi Ohtake, and Hua O. Wang
“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, Singapore,
Oct. 2007, pp. 160–165.
[8] H. Ichihara and E. Nobuyama, “A computational approach to state
feedback synthesis for nonlinear systems based on matrix sum of squares relaxations,” Proc. 17th Int’l Symposium on Mathematical
Theory of Network and Systems pp. 932–937, Kyoto, Japan, 2006.
[9] H. Ichihara, “Observer design for polynomial systems using convex
optimization,” in Proc. of the 46th IEEE CDC, New Orleans, LA,
Dec. 2007, pp. 5347–5352.
[10] X. Liu and Q. Zhang, “New approaches to H1 controller designs
based on fuzzy observers for T-S fuzzy systems via LMI,” Automatica,
vol. 39, pp. 1571–1582, 2003.
[11] 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, Kyoto, Japan, 2006, pp. 932–
937.
[12] 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, 2004, pp. 157–165.
[13] K. Tanaka, T. Hori and H.O. Wang “A multiple Lyapunov function
approach to stabilization of fuzzy control systems,” IEEE Transactions
on Fuzzy Systems, vol. 11, no. 4, pp. 582 – 589, Aug. 2003
[14] T. Takagi and M. Sugeno, “A systematic approach to improve multiple
Lyapunov function stability and stabilization conditions for
fuzzy systems,” Information Sciences, vol. 179, no. 8, pp. 1149–
1162, March 2009.
[15] Kazuo Tanaka, Hiroshi Ohtake, Toshiaki Seo, Motoyasu Tanaka,
Hua O Wang, “Polynomial fuzzy observer design: A sum-of-squares
approach.,” System, Man, and Cybernetics, Part B: Cybernetics,
IEEE Transactions on, 42(5):1330-1342, 2012.
[16] Antonio Sala, “Polynomial fuzzy models for nonlinear control: A
taylor series approach,” IEEE Trans on fuzzy systems, vol. 17,
no. 6, pp. 1284–1295, June 2009.
[17] J.R. Wan and J.C. Lo, “LMI relaxations for nonlinear fuzzy control
systems via homogeneous polynomials,” The 2008 IEEE World
Congress on Computational Intelligence, FUZZ2008, pp. 134—140,
Hong Kong, June 2008.
[18] V.F. Montagner and R.C.L.F Oliveira and P.L.D., “Necessary and
sufficient LMI conditions to compute quadratically stabilizing state
feedback controller for Takagi-Sugeno systems,” Proc. of the 2007
American Control Conference, pp. 4059–4064, July 2007.
[19] T. M. Guerra and L. Vermeiren, “LMI-based relaxed nonquadratic
stabilization conditions for nonlinear systems in the Takagi-
Sugeno’s form,” Automatica, vol. 40, pp. 823–829, 2004.
[20] B.C. Ding and H. Sun and P Yang, “Further studies on LMI-based
relaxed stabilization conditions for nonlinear systems in Takagi-
Sugeno’s form,” Automatica, vol. 43, pp. 503–508, August. 2006.
[21] X. Chang and G. Yang, “A descriptor representation approach to
observer-based H1 control synthesis for discrete-time fuzzy systems,”
Fuzzy Set and Systems, vol. 185, no. 1, pp. 38–51, 2010.
[22] B. Ding, “Homogeneous Polynomially Nonquadratic Stabilization of
Discrete-Time Takagi–Sugeno Systems via Nonparallel Distributed
Compensation Law,” IEEE Transactions on fuzzy systems vol. 18,
no. 5, pp. 994–1000, August 2010.
[23] J. Pan, S. Fei, A. Jaadari and T. M. Guerra, “Nonquadratic stabilization
of continuous T-S fuzzy models: LMI solution for local
approach,” IEEE Transactions on Fuzzy Systems, vol. 20, no. 3, pp.
594–602, 2012.
[24] D. H. Lee, J. B. Park and Y. H. Joo, “Approaches to extended
non-quadratic stability and stabilization conditions for discrete-time
Takagi-Sugeno fuzzy systems,” Automatica, vol. 47, no. 3, pp.534–
538, 2011.
[25] M. Johansson and A. Rantzer and K.-E. Arzen, “Piecewise
quadratic stability of fuzzy systems,” IEEE Transactions on fuzzy
systems, vol. 7, no. 6, pp. 713–722, December 1999.
[26] G. Feng, “Controller synthesis of fuzzy dynamic systems based on
piecewise Lyapunov functions,” IEEE Trans. Circuits and Syst. I:
Fundamental Theory and Applications, vol. 11, no. 5, pp. 605–612,
August 2003.
[27] G. Feng, C. Chen, D. Sun 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, vol. 13, no. 1, pp. 94–103,
2005.
[28] K. Tanaka and H. Yoshida and H. Ohtake and H. O. Wang, “A sum
of squares approach to modeling and control of nonlinear dynamical
systems with polynomial fuzzy systems,” IEEE Transactions on
fuzzy systems vol. 17, no. 4, pp. 911–922, August 2009.
[29] J. Xu and K.Y. Lum and et al, “A SOS-based approach to residual
generators for discrete-time polynomial nonlinear systems,” Proc.
of the 46th IEEE CDC, New Orleans pp. 372–344, December 2007.
[30] J. Xie, L. Xie and Y. Wang, “Synthesis of discrete-time nonlinear
systems: A SOS approach,” Proc. of the 2007 American Control
Conference New York, pp. 4829–4834, July 2007.
[31] K. Tanaka and H. Yoshida “Stabilization of polynomial fuzzy systems
via a sum of squares approach,” Proc. of the 22nd Int’l Symposium
on Intelligent Control Part of IEEE Multi-conference on
Systems and Control, pp. 160–165, Singapore, October, 2007.
[32] C.W.J. Hol and C.W. Scherer, “Sum of squares relaxations for
polynomial semidefinite programming,” Proc. of MTNS pp. 1–10,
2004.
[33] C. Ebenbauer and J. Renz and F. Allgower, “Polynomial feedback
and observer design using nonquadratic lyapunov functions,” 44th
IEEE Conference on Decision and Control, and the European Control
Conference, pp.7587–7592, 2005.
[34] K. Tanaka and H.O. Wang, “Fuzzy Control Systems Design and
Analysis: A Linear Matrix Inequality Approach,” pp. 69–76, New
York, NY, 2001.
[35] H.O. Wang and K. Tanaka and M.F. Griffin, “An approach to fuzzy
control of nonlinear systems: stability and design issues,” IEEE
Trans. Fuzzy Systems, vol. 4, no. 1, pp. 14–23, Feb. 1996.
[36] P.A. Parrilo, “Structured Semidefinite Programs and Semialgebraic
Geometry Methods in Robustness and Optimization,” Caltech,
Pasadena, CA, May 2000.
[37] Lin Xie, Serge Shishkin, and Minyue Fu,“Piecewise Lyapunov functions
for robust stability of linear time-varying systems,”Systems
Control Letters 31, pp. 165–171, 1997.
[38] V.A. Yakubovich, “S-procedures in nonlinear control theory,”Vest.
Leningr. Univ. 1, pp. 62-77, (1971).
[39] S. Boyd, L. El Ghaoui, E. Feron, V. Balakrishnan, “Linear Matrix
Inequalities in Systems and Control Theory,” SIAM monograph,
SIAM (1994).
[40] Ying-Jen Chen, Hiroshi Ohtake, Kazuo Tanaka, Wen-June Wang,
Hua O. Wang, “Relaxed stabilization criterion for T–S fuzzy systems
by minimum-type piecewise-Lyapunov-function-based switching
fuzzy controller,” IEEE Transactions on fuzzy systems, vol. 20,
No. 6, pp. 1166–1173, Dec, 2012.
[41] Ying-Jen Chen, Motoyasu Tanaka, Kazuo Tanaka, Hua O.
Wang, “Stability analysis and region-of-attraction estimation using
piecewise polynomial lyapunov functions: polynomial fuzzy
model approach,”IEEE Transactions on fuzzy systems, vol. 23, No.
4, pp, 1314–1322, August, 2015.
[42] Ali Chibani, Mohammed Chadli,and Naceur Benhadj Braiek, “A
sum of squares approach for polynomials fuzzy observer design for
polynomial fuzzy systems with unknowns input,” International Journal
of Control, Automation and Systems 14(1), pp.323–330, 2016.
[43] Kazuo Tanaka, Hiroshi Ohtake, Toshiaki Seo , Motoyasu Tanaka,
and Hua O. Wang “Polynomial fuzzy observer designs: a sum-ofsquares
approach,” IEEE Transactions on fuzzy systems,vol. 42, No.
5, pp. 1330–1342, 2012.
[44] Ji-Chang Lo ,and Chengwei Lin, “Polynomial fuzzy observed-state
feedback stabilization via homogeneous lyapunov methods, June
2015.
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指導教授 羅吉昌(J.C Lo) 審核日期 2017-8-25
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