連續模糊系統估測回授控制器非二次穩定性分析

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姓名

吳鎮宇(Chen-yu Wu) 查詢紙本館藏

畢業系所

機械工程學系

論文名稱

連續模糊系統估測回授控制器非二次穩定性分析
(Non-quadratic Stabilization Analysis for Observed-State Feedback Fuzzy Control)

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摘要(中)

本篇論文主要研究連續時間模糊(fuzzy)系統的非二次穩定寬鬆條件，我們利用波雅定理的代數性質加上寬鬆矩陣變數(slack matrix variables)，再利用激發強度的多項式排列控制器與估測器，並做控制與估測之相關分析，利用這些條件來建立一組寬鬆的線性矩陣不等式(LMI)並且降低求解的保守性。
論文還將透過非二次(non-quadratic)穩定的分析加上寬鬆矩陣變數(slack matrix variables)的使用，使得此組線性矩陣不等式(LMI)的求解保守性更進一步的降低，然後再將其中加入的寬鬆矩陣變數與波雅的線性矩陣不等式以多項式矩陣型態來表示，在判斷式子中加入了寬鬆矩陣變數，運用多項式矩陣型態之特性，將同階數的元素放在矩陣對角線上或同階數之非對角線上作變化，使判斷式保守度降低。

摘要(英)

In this thesis, we investigate non-quadratic relaxation for continuous-time fuzzy observed-state feedback control systems, which are characterized by parameter-dependent LMIs (PD-LMIs), exploiting the algebraic property of Polya Theorem to construct a family of finite-dimensional LMI relaxation with righ-hand-side slack matrices that release conservatism. And we use matrix-values HPPD function of degree g on Lyapunov function that release conservatism. Lastly, Numerical experiments illustrate this method can provide the advantage of relaxations, being less conservative and effective.

關鍵字(中)

★ T-S模糊控制系統
★ 估測回授控制器非二次穩定
★ 波雅定理
★ 寬鬆矩陣變數
★ 線性矩陣不等式

關鍵字(英)

★ Takagi-Sugeno fuzzy systems
★ Quadratic relaxations
★ Non-quadratic relaxations
★ Parameter-dependent LMIs (PD-LMIs)
★ Slack matrices
★ Polya Theorem

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、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. . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 符號標記. . . . . . . . . . . . . . . . . . . . . . . . 4
1.5 控制器與估測器的架構. . . . . . . . . . . . . . . . 6
1.6 預備定理. . . . . . . . . . . . . . . . . . . . . . . . 7
二、連續模糊閉迴路系統寬鬆穩定條件(共同李亞普諾夫
函數)................................................................................................... 9
2.1 系統的架構介紹. . . . . . . . . . . . . . . . . . . . 9
2.2 狀態回授控制器(Fuzzy systems) . . . . . . . . . . . 10
2.3 狀態估測器(Luenberger fuzzy observer) . . . . . . . 16
2.4 狀態估測回授控制器(Observed-state feedback controller)
. . . . . . . . . . . . . . . . . . . . . . . . . 20
三、連續模糊閉迴路系統之電腦模擬(共同李亞普諾夫函
數) ...................................................................................................... 28
3.1 系統1 架構. . . . . . . . . . . . . . . . . . . . . . 28
四、連續模糊閉迴路系統之寬鬆穩定條件(非共同李亞普
諾夫函數) ........................................................................................... 35
4.1 系統的架構. . . . . . . . . . . . . . . . . . . . . . . 35
4.1.1 多項式的組合方式. . . . . . . . . . . . . . . . . . . 36
4.2 狀態回授控制器(State feedback controlller) . . . . 36
iv
4.2.1 連續模糊閉迴路控制系統之穩定條件(非共同李亞
普諾夫函數) . . . . . . . . . . . . . . . . . . . . . . 37
4.2.2 非共同李亞普諾夫函數結合寬鬆矩陣變數. . . . . . 41
4.3 狀態回授估測器(Observed-state feedback) . . . . . 45
4.3.1 連續模糊閉迴路控制系統之穩定條件(非共同李亞
普諾夫函數) . . . . . . . . . . . . . . . . . . . . . . 45
4.3.2 非共同李亞普諾夫函數結合寬鬆矩陣變數. . . . . . 49
4.4 模糊連續估測回授控制系統(Observed-state feedback
controller) 之穩定條件. . . . . . . . . . . . . . 53
五、連續模糊閉迴路系統之電腦模擬(非共同李亞普諾夫
函數)................................................................................................... 61
5.1 系統1 架構. . . . . . . . . . . . . . . . . . . . . . 61
5.2 系統2 架構. . . . . . . . . . . . . . . . . . . . . . 73
六、結論與未來方向............................................................ 78
6.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . 78
6.2 未來方向. . . . . . . . . . . . . . . . . . . . . . . . 79
參考文獻............................................................................................. 80

參考文獻

[1] T. Taniguchi, K. Tanaka, H. Ohatake, and H.O. Wang. Model construction,
rule reduction and robust compensation for generalized
form of Takagi-Sugeno fuzzy systems. IEEE Trans. Fuzzy Systems,
9(4):525–538, August 2001.
[2] H.O. 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.
[3] K. Tanaka, T. Taniguchi, and H.O. Wang. Generalized Takagi-
Sugeno fuzzy systems: rule reduction and robust control. In Proc.
of 7th IEEE Conf. on Fuzzy Systems, 2000.
[4] H.O. Wang, K. Tanaka, and M.F. Griffin. An approach to fuzzy
control of nonlinear systems: stability and design issues. IEEE
Trans. Fuzzy Systems, 4(1):14–23, February 1996.
[5] K. Tanaka and H.O. Wang. Fuzzy Control Systems Design and
Analysis: A Linear Matrix Inequality Approach. John Wiley &
Sons, Inc., New York, NY, 2001.
[6] K. Tanaka, T. Ikeda, and H.O. Wang. Fuzzy regulators and
fuzzy observers: relaxed stability conditions and LMI-based designs.
IEEE Trans. Fuzzy Systems, 6(2):250–265, May 1998.
[7] J.C. Lo and M.L. Lin. Observer-based robust H∞ control for fuzzy
systems using two-step procedure. IEEE Trans. Fuzzy Systems,
12(3):350–359, June 2004.
[8] J.C. Lo and M.L. Lin. Robust H∞ nonlinear control via fuzzy static
output feedback. IEEE Trans. Circuits and Syst. I: Fundamental
Theory and Applications, 50(11):1494–1502, November 2003.
80
[9] M.C. de Oliveira, J. Bernussou, and J.C. Geromel. A new discretetime
robust stability condition. Syst. & Contr. Lett., 37:261–265,
1999.
[10] D. Peaucelle, D. Arzelier, O. Bachelier, and J. Bernussou. A new
robust D-stability condition for real convex polytopic uncertainty.
Syst. & Contr. Lett., 40:21–23, 2000.
[11] J.C. Geromel and M.C. de Oliveira. H2 and H∞ robust filtering for
convex bounded uncertain system. IEEE Trans. Automatic Control,
46(1):100–107, January 2001.
[12] M.C. de Oliveira, J.C. Geromel, and J. Bernussou. Extended H2
and H∞ norm characterizations and controller parameterizations
for discrete-time systems. Int. J. Contr., 75(9):666–679, 2002.
[13] 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., 55:52–61, January 2006.
[14] R.C.L.F Oliveira and P.L.D. Peres. Parameter-dependent LMIs
in robust analysis: characterization of homogeneous polynomially
parameter-dependent solutions via LMI relaxations. IEEE Trans.
Automatic Control, 52(7):1334–1340, July 2007.
[15] R.C.L.F Oliveira and P.L.D. Peres. LMI conditions for the existence
of polynomially parameter-dependent Lyapunov functions assuring
robust stability. In Proc. of 44th IEEE Conf. on Deci and Contr,
pages 1660–1665, Seville, Spain, December 2005.
[16] V.F. Montagner, R.C.L.F Oliveira, P.L.D. Peres, and P.-A. Bliman.
Linear matrix inequality characterization for H∞ and H2 guaranteed
cost gain-scheduling quadratic stabilization of linear timevarying
polytopic systems. IET Control Theory & Appl., 1(6):1726–
1735, 2007.
[17] V.F. Montagner, R.C.L.F Oliveira, and P.L.D. Peres. Necessary
and sufficient LMI conditions to compute quadratically stabilizing
state feedback controller for Takagi-sugeno systems. In Proc. of the
2007 American Control Conference, pages 4059–4064, July 2007.
81
[18] V.F. Montagner, R.C.L.F Oliveira, and P.L.D. Peres. Convergent
LMI relaxations for quadratic stabilization and H∞ control
of Takagi-sugeno fuzzy systems. IEEE Trans. Fuzzy Systems, (4):
863–873, August 2009.
[19] 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.
[20] 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.
[21] X.D. Liu and Q.L. Zhang. New approaches to H∞ controller designs
based on fuzzy observers for T-S fuzzy systems via LMI. Automatica,
39:1571–1582, June 2003.
[22] 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.
[23] B. Ding and B. Huang. Reformulation of LMI-based stabilization
conditions for non-linear systems in Takagi-Sugeno’s form. Int’l J.
of Systems Science, 39(5):487–496, 2008.
[24] T. M. Guerra and L. Vermeiren. Conditions for non quadratic stabilization
of discrete fuzzy models. In 2001 IFAC Conference, 2001.
[25] 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.
[26] J.R. Wan and J.C. Lo. LMI relaxations for nonlinear fuzzy control
systems via homogeneous polynomials. In The 2008 IEEE World
Congress on Computational Intelligence, FUZZ2008, pages 134–
140, Hong Kong, CN, June 2008.
[27] A. Sala and C. Arino. Asymptotically necessary and sufficient conditions
for stability and performance in fuzzy control: Applications
82
of Polya’s theorem. Fuzzy Set and Systems, 158:2671–2686, December
2007.
[28] R.C.L.F Oliveira and P.L.D. Peres. Stability of polytopes of matrices
via affine parameter-dependent Lyapunov functions: Asymptotically
exact LMI conditions. Linear Algebra and its Applications,
405:209–228, August 2005.
[29] K. Tanaka, T. Ikeda, and H.O. Wang. Robust stabilization of a
class of uncertain nonlinear systems via fuzzy control: quadratic
stabilizability, H∞ control theory, and linear matrix inequalities.
IEEE Trans. Fuzzy Systems, 4(1):1–13, February 1996.
[30] X.-J. Ma, Z.-Q. Sun, and Y.-Y. He. Analysis and design of fuzzy
controller and fuzzy observer. IEEE Trans. Fuzzy Systems, 6(1):41–
51, February 1998.
[31] J.C. Lo, C.H. Cho, and H.K. Lam. New LMI Formulation for
Observed-State Feedback Stabilization via SOS Relaxation. November.
under review.
[32] Huaguang. Zhang and Xiangpeng. Xie. Relaxed Stablity Conditions
for Continuous-Time T-S Fuzzy-Control Systems Via Augmented
Multi-Indexed Matrix Approach. pages 478–492, June 2011.
[33] J.C. Lo and C.F. Tsai. LMI relaxations for non-quadratic discrete
stabilization via Polya theorem. In Proc. of the 48th IEEE Conference
on Decision and Control, pages 7430–7435, Shanghai,CH,
December 2009.
[34] J.C. Lo and J.R. Wan. Studies on LMI relaxations for fuzzy control
systems via homogeneous polynomials. IET Control Theory &
Appl., 4(11):2293–2302, November 2010.
[35] J. Yoneyama, M. Nishikawa, H. Katayama, and A. Ichikawa. Output
stabilization of Takagi-Sugeno fuzzy systems. Fuzzy Set and
Systems, 111:253–266, April 2000.

指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2013-7-29

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