博碩士論文 88521035 詳細資訊




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:9 、訪客IP:18.206.194.83
姓名 孫崇訓(Chung-Hsun Sun)  查詢紙本館藏   畢業系所 電機工程學系
論文名稱 離散型T-S模糊系統的穩定條件放寬之研究
(Relaxed Stability Criteria for T-S Fuzzy Discrete Systems)
相關論文
★ 直接甲醇燃料電池混合供電系統之控制研究★ 利用折射率檢測法在水耕植物之水質檢測研究
★ DSP主控之模型車自動導控系統★ 旋轉式倒單擺動作控制之再設計
★ 高速公路上下匝道燈號之模糊控制決策★ 模糊集合之模糊度探討
★ 雙質量彈簧連結系統運動控制性能之再改良★ 桌上曲棍球之影像視覺系統
★ 桌上曲棍球之機器人攻防控制★ 模型直昇機姿態控制
★ 模糊控制系統的穩定性分析及設計★ 門禁監控即時辨識系統
★ 桌上曲棍球:人與機械手對打★ 麻將牌辨識系統
★ 相關誤差神經網路之應用於輻射量測植被和土壤含水量★ 三節式機器人之站立控制
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]
  1. 本電子論文使用權限為同意立即開放。
  2. 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。
  3. 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) 基於李亞普諾夫穩定定理(Lyapunov stability criterion),保證離散型T-S模糊系統穩定的充分條件,就是找到一個共同P矩陣滿足系統中所有李亞普諾夫不等式(Lyapunov inequality)。一般而言,這個共同P矩陣可藉由線性矩陣不等式(LMI)的求解法所求得。然而,當模糊系統中的規則數過多時,即使是使用線性矩陣不等式的軟體工具,也不一定能求得這個共同P矩陣。近來,為了解決這個問題,許多學者改以片段連續型李亞普諾夫二次式(piecewise quadratic Lyapunov function)和權重相依型李亞普諾夫二次式(weighting dependent Lyapunov function)來推導離散型T-S模糊系統的穩定條件。理論上來說,以這兩種李亞普諾夫二次式所推導出的穩定條件會較為寬鬆,但是這兩種李亞普諾夫二次式卻會導至較多的李亞普諾夫不等式。所以,在本篇論文中,我們藉由分析模糊系統中的狀態位置資訊來減少李亞普諾夫不等式的數量,以達到穩定條件放寬之目的。
在第三章和第四章中,藉由觸發規則群的觀念和狀態間距概念的分析,我們可獲知以前學者所提出的穩定條件中,某些李亞普諾夫不等式其實是不必要的,因此若能扣除這些多餘的李亞普諾夫不等式,則可得到較寬鬆的穩定條件。在第五章中,除了之前提到的兩個概念外,又引入頂點表示法(vertex expression)來描述觸發規則群的空間大小,這使我們能夠找出更多不需要的李亞普諾夫不等式,更放寬了原有的穩定條件。此外,在第三、四、五章的最後,藉由數值的例子與定理的比較,可證明我們所提出的理論確實具有放寬穩定條件的效能。
摘要(英) It is well known that the first stability criterion for Takagi-Sugeno (T-S) fuzzy discrete system is derived from the common quadratic Lyapunov function. That is to find a common matrix P to satisfy all Lyapunov inequalities. Then the stability of T-S fuzzy discrete systems can be guaranteed. In general, the common matrix can be found by means of linear matrix inequalities (LMI) method. However, if the number of rules of a fuzzy system is large, the common matrix P may not exist or may not be found even using LMI. Recently, the piecewise quadratic Lyapunov function and the weighting dependent Lyapunov function are employed instead of the common quadratic Lyapunov function. It is believed that the above two Lyapunov functions derive more relaxed stability criteria than the common quadratic Lyapunov function does. However they induce more Lyapunov inequalities to be satisfied. In this dissertation, more relaxed stability criteria for T-S fuzzy discrete systems are proposed. They are based on the piecewise quadratic Lyapunov function and the weighting dependent Lyapunov function respectively. This dissertation combines the ideas of group-fired rules, the width of states step and the vertex expression together, so that the relaxed stability criteria need to satisfy fewer Lyapunov inequalities. In each chapter, some numerical examples and comparisons are presented to show the effectiveness of this work.
關鍵字(中) ★ T-S 模糊系統
★ 穩定性
★ 條件放寬
關鍵字(英) ★ stability
★ relaxed conditions
★ T-S fuzzy system
論文目次 Abstract I
List of Figures V
List of Tables VI
Chapter 1 Introduction
1.1 Motivation and background 1
1.2 Review of previous works 2
1.3 Organization and main tasks 5
Chapter 2 Problem Formulations and Previous Criteria Review
2.1 Introduction 7
2.2 T-S fuzzy discrete system and its Lyapunov stability 9
2.2.1 T-S fuzzy system 9
2.2.2 Lyapunov stability based on a common quadratic function 11
2.2.3 Lyapunov stability based on a piecewise quadratic function 13
2.2.4 Lyapunov stability based on a weighting dependent function 15
2.3 Existence conditions of Lyapunov functions 16
2.4 Summary 18
Chapter 3 Relaxed Lyapunov Stability Criteria based on Piecewise Quadratic Functions
3.1 Introduction 19
3.2 Relaxed stability criteria via maximum step width of states 20
3.2.1 Concept of group-fired rules 21
3.2.2 Stability criteria with boundary conditions 24
3.2.3 Maximum step width of two successive states 26
3.2.4 Relaxed stability and stabilization conditions 29
3.3 Numeric examples 34
3.4 Summary 38
Chapter 4 Relaxed Lyapunov Stability Criterion based on a Weighting Dependent Function
4.1 Introduction 40
4.2 Relaxed stability criteria via maximum step width of states 41
4.2.1 Maximum step width of two successive states 41
4.2.2 Concept of group-fired rules 44
4.2.3 Relaxed stability criterion 47
4.3 Numeric example 49
4.4 Summary 52
Chapter 5 An Improved Stability Criterion via Vertex Expression
5.1 Introduction 54
5.2 Preliminary 55
5.2.1 T-S fuzzy discrete system 55
5.2.2 Stability based on weighting dependent Lyapunov function 56
5.3 Relaxed stability criteria via the information of antecedents 58
5.3.1 Switching fuzzy systems and the vertex expression 58
5.3.2 Step widths of two successive states 60
5.3.3 Relaxed stability criterion 64
5.4 Numeric example 67
5.5 Summary 73
Chapter 6 Conclusions and Future Works
6.1 Conclusions 74
6.2 Future works 75
Reference 76
Publication List 84
參考文獻 [1] K. J. Astrom, and B. Wittenmark, Computer controlled systems: theorem and design, Prentice-Hall, 1984.
[2] S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear matrix inequalities in systems and control theory, SIAM., Philadelphia, PA, 1994.
[3] S. G. Cao, N. W. Rees, and G. Feng, “Quadratic stability analysis and design of continuous-time fuzzy control systems,” Int. Journal of Syst. Science, vol. 27, pp. 193-203, 1996.
[4] S. G. Cao, N. W. Rees, and G. Feng, “Stability analysis and design for a class of continuous-time fuzzy control systems,” Int. Journal of Contr., vol. 64, pp. 1069-1087, 1996.
[5] S. G. Cao, N. W. Rees, and G. Feng, “Lyapunov-like stability theorems for discrete-time fuzzy control systems,” Int. Journal of Syst. Science, vol. 28, pp. 297-308, 1997.
[6] S. G. Cao, N. W. Rees, and G. Feng, “Further results about quadratic stability of continuous-time fuzzy control systems”, Int. Journal of Syst. Science, vol. 28, pp. 397-404, 1997.
[7] S. G. Cao, N. W. Rees, and G. Feng, “Analysis and design of fuzzy control systems using dynamic fuzzy-state space models,” IEEE Trans. on Fuzzy Syst., vol. 7, pp. 192-200, 1999.
[8] M. Chadli, D. Maquin, and J. Ragot, “Relaxed stability conditions for Takagi-Sugeno fuzzy systems,” in Proc. IEEE Int. Conf., Syst., Man, Cybern., 2000, pp. 3514-3519.
[9] C. L. Chen, P. C. Chen, and C. K. Chen, “Analysis and design of fuzzy control systems,” Fuzzy Sets and Syst., vol. 57, pp.125-140, 1993.
[10] D. J. Choi, P. G. Park, “State-feedback controller design for discrete-time switching fuzzy systems,” in Proc. IEEE Conf. Decision and Contr., 2002, pp. 191-196.
[11] D. J. Choi, P. G. Park, “ controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions,” in Proc. Americen Contr. Conf., 2002, pp. 3252-3257.
[12] D. J. Choi, P. G. Park, “ state-feedback controller design for discrete-time fuzzy systems using fuzzy weighting-dependent Lyapunov functions,” IEEE Trans. Fuzzy Syst., vol. 11, pp. 271-278, 2003.
[13] D. J. Choi, P. G. Park, “Guaranteed cost controller design for discrete-time switching fuzzy system,” IEEE Trans. Syst., Man, and Cybern., B, vol. 34, pp. 110-119, 2004.
[14] J. Daafouz, and J. Bernussou, “Parameter dependent Lyapunov functions for discrete time systems with varying parametric uncertainties,” Syst., and Contr. Lett., pp. 355-359, 2001.
[15] J. Daafouz, P. Riedinger, and C. Lung, “Stability analysis and control synthesis for switched systems: a switched Lyapunov function approach” IEEE Trans. Automat. Contr., vol. 47, pp.1883-1887, 2002.
[16] G. Feng, S. G. Cao, N. W. Rees, and C. K. Chak, “Design of fuzzy control systems with guaranteed stability,” Fuzzy Sets and Syst., vol. 85, pp. 1-10, 1997.
[17] M. Feng, and C. J. Harris, “Piecewise Lyapunov stability conditions of fuzzy systems” IEEE Trans. Syst., Man, and Cybern., B, vol. 31, pp. 259-262, 2001.
[18] P. Gahinet, A. Nemirovski, A. Laub, and M. Chilali, LMI control toolbox, The Math Works Inc., 1994.
[19] T. M. Guerra, and W. Perruquetti, “Non quadratic stabilization of discrete fuzzy models,” in Proc. IEEE Int. Conf., Fuzzy Syst., 2001, pp. 1271-1274.
[20] T. M. Guerra and L. Vermeiren, “Control laws for Takagi-Sugeno fuzzy models,” Fuzzy Sets and Syst., vol. 120, pp. 95-108, 2001.
[21] C. C. Hsiao, S. F. Su, T. T. Lee and C. C. Chuang, “Hybrid compensation control for affine TSK fuzzy control systems,” IEEE Trans. Syst., Man, Cybern. B, vol. 34, pp. 1865-1872, 2004.
[22] C. P. Huang, “Stability analysis of discrete singular fuzzy systems,” Fuzzy Sets and Syst., vol. 151, pp. 155-165, 2005.
[23] M. Johansson, A. Rantzer, and K. E. Årzén, “Piecewise quadratic stability of fuzzy systems” IEEE Trans. Fuzzy Syst., vol. 7, pp. 713-722, 1999.
[24] H. Kiendl, and J. J. Rűger, “Stability analysis of fuzzy control systems using facet functions” Fuzzy Sets and Syst., vol. 70, pp. 275-285, 1995.
[25] E. Kim and S. Kim, “Stability analysis and synthesis for an affine fuzzy control system via LMI and ILMI: Continuous case” IEEE Trans. Fuzzy Syst., vol. 10, pp. 391-400, 2002.
[26] E. Kim, and H. Lee, “New approaches to relaxed quadratic stability condition of fuzzy control systems,” IEEE Trans. Fuzzy Syst., vol. 8, pp. 523-533, 2000.
[27] K. Kiriakidis, “Robust stabilization of the Takagi-Sugeno fuzzy model via bilinear matrix inequalities,” IEEE Trans. Fuzzy Syst., vol. 9, pp. 269-277, 2001.
[28] H. K. Lam, F. H. F. Leung and P. K. S. Tam, “Nonlinear State Feedback Controller for Nonlinear Systems: Stability Analysis and Design Based on Fuzzy Plant Model,” IEEE Trans. Fuzzy Syst., vol. 9, pp. 657-661, 2001.
[29] H. K. Lam, F. H. F. Leung and P. K. S. Tam, “Design and Stability Analysis of Fuzzy Model-Based Nonlinear Controller for Nonlinear Systems Using Genetic Algorithm,” in Proc. IEEE Int. Conf., Fuzzy Syst., 2002, pp.232-237.
[30] H. K. Lam, F. H. F. Leung and P. K. S. Tam, “Design and Stability Analysis of Fuzzy Model-Based Nonlinear Controller for Nonlinear Systems Using Genetic Algorithm,” IEEE Trans. Syst., Man, and Cybern., B, vol. 33, pp. 250-257, 2003.
[31] H. K. Lam, P. K. S. Tam and F. H. F. Leung, “A linear matrix inequality approach for the control of uncertain fuzzy systems” IEEE Contr. Syst. Magazine, vol. 22, pp. 20-25, 2002.
[32] F. H. F. Leung, L. K. Wong and P. K. S. Tam, “Fuzzy model based controller for an inverted pendulum” Electron. Lett., vol. 32, pp. 1683-1685, 1996.
[33] D. Mignone, G. Ferrari-Trecate, and M. Morari, “Stability and stabilization of piecewise affine and hybrid systems: An LMI approach,” in Proc. IEEE Conf. Decision and Contr., 2000, pp. 504-509.
[34] H. Ohtake, K. Tanaka, and H. O. Wang, “A construction method of switching Lyapunov function for nonlinear systems,” in Proc. IEEE Int. Conf., Fuzzy Syst., 2002, pp. 221-226.
[35] C. T. Pang, and S. M. Guu, “Sufficient conditions for the stability of linear Takagi-Sugeno free fuzzy systems,” IEEE Trans. Fuzzy Syst., vol. 11, pp. 695-700, 2003.
[36] M. Sugeno, “On stability of fuzzy systems expressed by fuzzy rules with singleton consequents,” IEEE Trans. Fuzzy Syst., vol. 7, pp. 201-224, 1999.
[37] M. Sugeno and G. T. Kang, “Structure identification of fuzzy model,” Fuzzy Sets and Syst., vol. 18, pp. 329-346, 1986.
[38] C. H. Sun and W. J. Wang, “A stability criterion for discrete T-S fuzzy systems without global common P,” in Proc. 2003 Chinese Automat. Contr. Conf. and Bio-Mechatronics Syst. Contr. and Application Workshop, 2003, pp. 215-219.
[39] C. H. Sun and W. J. Wang, “A Weighting Dependent Lyapunov Function Based Relaxed Stability Criterion for T-S Fuzzy Discrete Systems,” in Proc. Chinese Automat. Contr. Conf., 2004.
[40] T. Takagi, and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and conrol,” IEEE Trans. Syst., Man, Cybern. B, vol. 15, pp. 116-132, 1985.
[41] K. Tanaka, T. Hori, and H. O. Wang, “A multiple Lyapunov Function approach to stabilization of fuzzy control systems,” IEEE Trans. Fuzzy Syst., vol. 11, pp. 582-589, 2003.
[42] K. Tanaka, T. Ikeda, and H. O. Wang, “Robust stabilization of a class of uncertain nonlinear systems via fuzzy control: quadratic stabilizability, control theory, and linear matrix inequalities,” IEEE Trans. Fuzzy Syst., vol. 4, pp. 1-13, 1996.
[43] K. Tanaka, T. Ikeda, and H. O. Wang, “An LMI approach to fuzzy controller designs based on relaxed stability conditions” in Proc. IEEE Int. Conf., Fuzzy Syst., 1997, pp.171-176.
[44] K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy regulators and fuzzy observers: Relaxed stability conditions and LMI-based designs,” IEEE Trans. Fuzzy Syst., vol. 6, pp. 250-265, 1998.
[45] K. Tanaka, M. Iwasaki, and H. O. Wang, “Stable switching fuzzy control and its application to a hovercraft type vehicle,” in Proc. IEEE Int. Conf., Fuzzy Syst., 2000, pp. 804-809.
[46] K. Tanaka, M. Iwasaki, and H. O. Wang, “Stability and smoothness conditions for switching fuzzy systems,” in Proc. American Contr. Conf., 2000, pp. 2474-2478.
[47] K. Tanaka, M. Iwasaki, and H. O. Wang, “Switching control of an R/C hovercraft: stabilization and smooth switching” IEEE Trans. Syst., Man, and Cybern. B, vol. 31, pp. 853-863, 2001.
[48] K. Tanaka, and M. Sano, “A robust stabilization problem of fuzzy control systems and its application to backing up control of a truck-trailer,” IEEE Trans. Fuzzy Syst., vol. 2, pp.119-134, 1994.
[49] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control system,” Fuzzy Sets and Syst., vol. 45, pp. 135-156, 1992.
[50] M. C. M. Teixeira, and S. H. Żak, “Stabilizing controller design for uncertain nonlinear system using fuzzy models,” IEEE Trans. Fuzzy Syst., vol. 7, pp. 133-142, 1999.
[51] M. C. M. Teixeira, E. Assunção, and R. G. Avellar, “On relaxed LMI-based designs for fuzzy regulators and fuzzy observers,” IEEE Trans. Fuzzy Syst., vol. 11, pp. 613-623, 2003.
[52] M. A. L. Thathachar, and P. Viswanath, “On the stability of fuzzy systems,” IEEE Trans. Fuzzy Syst., vol. 5, pp. 145-151, 1997.
[53] H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto, “Parameterized linear matrix inequality techniques in fuzzy control system design,” IEEE Trans. Fuzzy Syst., vol. 9, pp. 324-332, 2001.
[54] H. O. Wang, K. Tanaka and M. F. Griffin, “An approach to fuzzy control of nonlinear system: Stability and design issues,” IEEE Trans. Fuzzy Syst., vol. 4, pp. 14-23, 1996.
[55] L. Wang, and G. Feng, “Piecewise controller design of discrete time fuzzy systems,” IEEE Trans. Syst., Man, Cybern. B, vol. 34, pp. 682-686, 2004.
[56] L. X. Wang, A course in fuzzy systems and control, Prentice-Hall, 1997.
[57] W. J. Wang, and C. S. Sun, “Relaxed stability condition for T-S fuzzy discrete system,” in Proc. IEEE Int. Conf., Fuzzy Syst., 2002, pp. 244-249.
[58] W. J. Wang, C. S. Sun, and L. Luoh, “Relaxed stability conditions for T-S fuzzy systems,” in Proc. 9th IFSA World Congress and 20th NAFIPS, Int. Conf., 2001, pp. 221-226.
[59] W. J. Wang, and C. H. Sun, “A Relaxed stability criterion for T-S fuzzy discrete system,” IEEE Trans. Syst., Man, and Cybern. B, vol. 34, pp. 2155-2158, 2004.
[60] W. J. Wang, and C. H. Sun, “A Relaxed stability criterion for T-S fuzzy discrete systems,” in Proc. Int. Conf. on Networking, Sensing and Contr., 2004, pp. 937-942.
[61] W. J. Wang and C. H. Sun, “A Weighting Dependent Lyapunov Function Based Relaxed Stability Criterion for T-S Fuzzy Discrete Systems,” in Proc. Int. Conf. Networking, Sensing and Contr., 2005, pp. 135-140.
[62] W. J. Wang and L. Luoh, “Alternative Stabilization Design for Fuzzy Systems,” Electron. Lett., vol. 37, pp. 601-603, 2001.
[63] W. J. Wang, S. F. Yang and C. H. Chiu, “Flexible stability criteria for a linguistic fuzzy dynamic system” Fuzzy Sets and Syst., vol.105, pp. 63-80, 1999.
[64] L. A. Zadeh, “Outline of a new approach to the analysis of complex systems and decision processes,” IEEE Trans. IEEE Trans. Syst., Man, and Cybern., vol. 3, pp. 28-44, 1973.
[65] S. H. Żak, “Stability fuzzy system models using linear controllers,” IEEE Trans. Fuzzy Syst., vol. 7, pp. 236-240, 1999.
指導教授 王文俊(Wen-June Wang) 審核日期 2006-1-17
推文 facebook   plurk   twitter   funp   google   live   udn   HD   myshare   reddit   netvibes   friend   youpush   delicious   baidu   
網路書籤 Google bookmarks   del.icio.us   hemidemi   myshare   

若有論文相關問題,請聯絡國立中央大學圖書館推廣服務組 TEL:(03)422-7151轉57407,或E-mail聯絡  - 隱私權政策聲明