切換式靜態輸出回授控制—齊次李亞普諾夫法

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梁恩晟(En-Chen Liang) 查詢紙本館藏

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機械工程學系

論文名稱

切換式靜態輸出回授控制—齊次李亞普諾夫法
(Switching Static Output Feedback Controller for Polynomial Fuzzy Systems via Homogeneous Lyapunov Functions)

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摘要(中)

本論文探討多項式模糊系統之切換式靜態輸出回授控制器設計，包含了連續時間系統及離散時間系統。藉由最小型片段式李亞普諾夫函數作穩定性分析，其型式為V(x)=min_{1leq l leq N}ig{V_l(x)ig}，
片段式李亞普諾夫函數亦為控制器切換的依據。在連續時間系統中，為了解決非凸項$dot P(x)$的問題，使用尤拉齊次多項式定理來建立片段函數
V_l(x)=x^TP_l(x)x=frac{1}{g(g-1)}x^T abla_{xx}V_l(x)x
在離散系統中，為了避免未知數的影響，以利電腦模擬順利進行，本論文將片段函數定義為V_l(x)=x^TP_l^{-1}( ilde x)x，
其中$ ilde x$是不受控制力直接影響的狀態集合，在文中有詳細說明。

在電腦模擬中，使用了平方和方法檢測穩定性條件，並設計出切換式靜態輸出回授控制器。

摘要(英)

In this paper, we study switching static output feedback control problem for both continuous- and discrete-time polynomial fuzzy systems.
The stabilization of the systems is proved with minimum-type piecewise Lyapunov functions, which have the form V(x)=min_{1leq l leq N}ig{V_l(x)ig}.
Switching mechanism of the controllers is also based on piecewise Lyapunov functions. In continuous-time systems, in order to remove non-convex term dot P(x), via Euler′s theorem for homogeneous functions we establish piecewise functions as follows.
V_l(x)=x^TP_l(x)x=frac{1}{g(g-1)}x^T abla_{xx}V_l(x)x
In discrete-time systems, the piecewise functions are defined as V_l(x)=x^TP_l^{-1}( ilde x)x$ to prevent problems where ilde x is the set of states whose corresponding row in B_i(x) are empty. Further details are described in the text.

In numerical examples, stability conditions and controller synthesis are tested and solved via sum-of-squares approach.

關鍵字(中)

★ 平方和(sum of squares)
★ 多項式模糊系統(polynomial fuzzy systems)
★ 尤拉齊次多項式定理(Euler′s Theorem for Homogeneous Functions)
★ 切換式靜態輸出回授控制(switching static output feedback control)
★ 最小型片段式李亞普諾夫函數(minimum-type piecewise Lyapunov functions)

關鍵字(英)

★ Sum of squares
★ Polynomial fuzzy systems
★ Euler′s Theorem for Homogeneous Functions
★ Switching static output feedback control
★ Minimum-type piecewise Lyapunov functions

論文目次

摘要.......................................................................................... v
Abstract......................................................................................... vi
誌謝.................................................................................................vii
目錄.................................................................................................viii
圖目錄.............................................................................................. x
一、緒論..................................................................... 1
1.1 文獻回顧. . . . . . . . . . . . . . . . . . . . . . . 1
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . 3
1.3 論文結構. . . . . . . . . . . . . . . . . . . . . . . 4
1.4 符號標記. . . . . . . . . . . . . . . . . . . . . . . 4
1.5 預備定理. . . . . . . . . . . . . . . . . . . . . . . 6
二、系統架構與主要定理................................................... 14
2.1 模糊系統架構簡介. . . . . . . . . . . . . . . . . . . . . . . 14
2.2 切換式多項式輸出回授控制器. . . . . . . . . . . . 15
2.3 主要定理. . . . . . . . . . . . . . . . . 16
三、模糊建模方法及平方和檢測法....................................25
3.1 泰勒級數模糊法. . . . . . . . . . . . . . . . . . . . . 25
3.2 平方和檢測法. . . . . . . . . . . . . . . . . . . . . 29
四、電腦模擬.....................................................................32
4.1 例題一. . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 例題二. . . . . . . . . . . . . . . . . . . . . . . . . 41
4.3 例題三. . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 例題三. . . . . . . . . . . . . . . . . . . . . . . . . 57
五、結論與未來方向..........................................................64
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.2 未來研究方向. . . . . . . . . . . . . . . . . . . . . 65
參考文獻..........................................................66

參考文獻

[1] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its applications to modeling and control,” IEEE Transactions on Systems, Man, and Cybernetics, vol. SMC-15, pp. 116–132, Jan 1985.
[2] K. Tanaka and M. Sugeno, “Stability analysis and design of fuzzy control systems,” Fuzzy Sets and Systems, vol. 45, no. 2, pp. 135 – 156, 1992.
[3] K. Tanaka, T. Ikeda, and H. O. Wang, “Fuzzy regulators and fuzzy observers: relaxed stability conditions and lmi-based designs,” IEEE Transactions on Fuzzy Systems, vol. 6, pp. 250–265, May 1998.
[4] M. de Oliveira, J. Bernussou, and J. Geromel, “A new discrete-time robust stability condition,” Systems & Control Letters, vol. 37, no. 4, pp. 261 – 265, 1999.
[5] EuntaiKimandHeejinLee,“Newapproachestorelaxedquadraticstabilitycondition of fuzzy control systems,” IEEE Transactions on Fuzzy Systems, vol. 8, pp. 523–534, Oct 2000.
[6] L. Xiaodong and Z. Qingling, “New approaches to H∞ controller designs based on fuzzy observers for t-s fuzzy systems via lmi,” Automatica, vol. 39, no. 9, pp. 1571 – 1582, 2003.
[7] V. C. S. Campos, F. O. Souza, L. A. B. Tôrres, and R. M. Palhares, “New sta- bility conditions based on piecewise fuzzy lyapunov functions and tensor product transformations,” IEEE Transactions on Fuzzy Systems, vol. 21, pp. 748–760, Aug 2013.
[8] 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, pp. 582–589, Aug 2003.
[9] J.Li,S.Zhou,andS.Xu,“Fuzzycontrolsystemdesignviafuzzylyapunovfunctions,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 38, pp. 1657–1661, Dec 2008.
[10] A. Ibtissem, N. Golea, and M. Hadjili, “A new fuzzy lyapunov approach to non- quadratic stabilization of takagi-sugeno fuzzy models,” Int. J. Appl. Math. Comput. Sci., vol. 17, p. 39?51, 01 2007.
66
[11] B. Ding, H. Sun, and P. Yang, “Further studies on lmi-based relaxed stabilization conditions for nonlinear systems in takag?i sugeno’s form,” Automatica, vol. 42, no. 3, pp. 503 – 508, 2006.
[12] M. Johansson, A. Rantzer, and K. E. Arzen, “Piecewise quadratic stability of fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 7, pp. 713–722, Dec 1999.
[13] Gang Feng, “Stability analysis of discrete-time fuzzy dynamic systems based on piecewise lyapunov functions,” IEEE Transactions on Fuzzy Systems, vol. 12, pp. 22– 28, Feb 2004.
[14] J. Qiu, G. Feng, and H. Gao, “Fuzzy-model-based piecewise H∞ static-output- feedback controller design for networked nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 18, pp. 919–934, Oct 2010.
[15] J. Qiu, G. Feng, and H. Gao, “Static-output-feedback ∞ control of continuous-time t - s fuzzy affine systems via piecewise lyapunov functions,” IEEE Transactions on Fuzzy Systems, vol. 21, pp. 245–261, April 2013.
[16] L. A. Mozelli, R. M. Palhares, and G. S. Avellar, “A systematic approach to improve multiple lyapunov function stability and stabilization conditions for fuzzy systems,” Information Sciences, vol. 179, no. 8, pp. 1149 – 1162, 2009.
[17] L. Xie, S. Shishkin, and M. Fu, “Piecewise lyapunov functions for robust stability of linear time-varying systems,” Systems & Control Letters, vol. 31, no. 3, pp. 165 – 171, 1997.
[18] Y.-J. Chen, H. Ohtake, K. Tanaka, W.-J. Wang, and H. Wang, “H∞ control of t-s fuzzy systems using piecewise lyapunov function based switching fuzzy controller,” pp. 3087 – 3092, 01 2010.
[19] Y.J.Chen,H.Ohtake,K.Tanaka,W.J.Wang,andH.O.Wang,“Relaxedstabiliza- tion criterion for t-s fuzzy systems by minimum-type piecewise-lyapunov-function- based switching fuzzy controller,” IEEE Transactions on Fuzzy Systems, vol. 20, pp. 1166–1173, Dec 2012.
[20] Y. Chen, M. Tanaka, K. Tanaka, and H. 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, pp. 1314–1322, Aug 2015.
[21] K. Tanaka, H. Yoshida, H. Ohtake, and H. O. Wang, “A sum of squares approach to stability analysis of polynomial fuzzy systems,” in 2007 American Control Con- ference, pp. 4071–4076, July 2007.
[22] 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 sys- tems,” IEEE Transactions on Fuzzy Systems, vol. 17, pp. 911–922, Aug 2009.
67

[23] A. Sala and C. AriÑo, “Polynomial fuzzy models for nonlinear control: A taylor series approach,” IEEE Transactions on Fuzzy Systems, vol. 17, pp. 1284–1295, Dec 2009.
[24] R. Chaibi and A. Hmamed, “Static output feedback control problem for polynomial fuzzy systems via a sum of squares (sos) approach,” in 2017 Intelligent Systems and Computer Vision (ISCV), pp. 1–6, April 2017.
[25] T. González, M. Bernal, A. Sala, and B. Aguiar, “Cancellation-based nonquadratic controller design for nonlinear systems via takagi?sugeno models,” IEEE Transac- tions on Cybernetics, vol. 47, pp. 2628–2638, Sep. 2017.
[26] S.-W. Kau, H.-J. Lee, C.-M. Yang, C.-H. Lee, L. Hong, and C.-H. Fang, “Robust H∞ fuzzy static output feedback control of t-s fuzzy systems with parametric uncer- tainties,” Fuzzy Sets and Systems, vol. 158, pp. 135–146, 01 2007.
[27] C. M. Agulhari, R. C. L. F. Oliveira, and P. L. D. Peres, “Static output feedback control of polytopic systems using polynomial lyapunov functions,” in 49th IEEE Conference on Decision and Control (CDC), pp. 6894–6901, Dec 2010.
[28] C. M. Agulhari, R. C. L. F. Oliveira, and P. L. D. Peres, “Robust H∞ static output- feedback design for time-invariant discrete-time polytopic systems from parameter- dependent state-feedback gains,” in Proceedings of the 2010 American Control Con- ference, pp. 4677–4682, June 2010.
[29] E. S. Tognetti, R. C. L. Oliveira, and P. L. Peres, “An lmi-based approach to static output feedback stabilization of t?s fuzzy systems,” IFAC Proceedings Volumes, vol. 44, no. 1, pp. 12593 – 12598, 2011. 18th IFAC World Congress.
[30] X.-H. Chang, L. Zhang, and J. H. Park, “Robust static output feedback h∞ control for uncertain fuzzy systems,” Fuzzy Sets and Systems, vol. 273, pp. 87 – 104, 2015. Theme: Control Engineering.
[31] L. Zadeh, “Fuzzy sets,” Information and Control, vol. 8, no. 3, pp. 338 – 353, 1965.
[32] E. Mamdani and S. Assilian, “An experiment in linguistic synthesis with a fuzzy logic controller,” International Journal of Man-Machine Studies, vol. 7, no. 1, pp. 1 – 13, 1975.
[33] Ji-Chang Lo and Min-Long Lin, “Robust H∞ nonlinear control via fuzzy static out- put feedback,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 50, pp. 1494–1502, Nov 2003.
[34] J. Lo and C. Lin, “Polynomial fuzzy observed-state feedback stabilization via homo- geneous lyapunov methods,” IEEE Transactions on Fuzzy Systems, vol. 26, pp. 2873– 2885, Oct 2018.
[35] S. Prajna, A. Papachristodoulou, and P. A. Parrilo, “Introducing sostools: a gen- eral purpose sum of squares programming solver,” in Proceedings of the 41st IEEE Conference on Decision and Control, 2002., vol. 1, pp. 741–746 vol.1, Dec 2002.
[36] C. Ebenbauer, J. Renz, and F. Allgower, “Polynomial feedback and observer design using nonquadratic lyapunov functions,” in Proceedings of the 44th IEEE Conference on Decision and Control, pp. 7587–7592, Dec 2005.
[37] S. Boyd, L. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory. Studies in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM, 3600 Market Street, Floor 6, Philadelphia, PA 19104), 1994.
[38] S. Prajna, A. Papachristodoulou, and Fen Wu, “Nonlinear control synthesis by sum of squares optimization: a lyapunov-based approach,” in 2004 5th Asian Control Conference (IEEE Cat. No.04EX904), vol. 1, pp. 157–165 Vol.1, July 2004.
[39] K. Tanaka, H. Ohtake, T. Seo, M. Tanaka, and H. O. Wang, “Polynomial fuzzy observer designs: A sum-of-squares approach,” IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), vol. 42, pp. 1330–1342, Oct 2012.
[40] H. Zhang, C. Qin, B. Jiang, and Y. Luo, “Online adaptive policy learning algorithm for H∞ state feedback control of unknown affine nonlinear discrete-time systems,” IEEE Transactions on Cybernetics, vol. 44, pp. 2706–2718, Dec 2014.
[41] H. Li, J. Wang, and P. Shi, “Output-feedback based sliding mode control for fuzzy systems with actuator saturation,” IEEE Transactions on Fuzzy Systems, vol. 24, pp. 1282–1293, Dec 2016.
[42] A. A. Ahmadi and A. Majumdar, “Dsos and sdsos optimization: Lp and socp-based alternatives to sum of squares optimization,” in 2014 48th Annual Conference on Information Sciences and Systems (CISS), pp. 1–5, March 2014.

指導教授

羅吉昌(Ji-Chang Lo)

審核日期

2019-7-24

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