臺灣博碩士論文加值系統

在這個研究裡，非線性隨機系統對於參數時變的問題，我們提供了一個模糊轉換穩定度的方法藉由輸出回授控制。多模組轉換方法已經被使用去處理線性時變參數系統。換言之，Takagi-Sugeno (TS) 模糊建模系統通常被使用去近似非線性非時變系統。結合多模組轉換方法和模糊建模系統，並且利用模糊輸出回授控制和模糊轉換建模系統被提供去對付非線性時變隨機系統穩定度的問題。為了去降低近似誤差和外部干擾的影響， 模糊觀測狀態回饋轉換控制可以最小化估測誤差的 所規範的 上界在 的規範在一個被期許的值之下。在這些條件之下， 模糊觀測狀態回饋轉換控制能夠被改善藉由線性矩陣不等式 (LMIs), 線性矩陣不等式能夠允許convex最佳化過程去解決非線性時變的強健 控制問題。最後，模擬例子是被提供的去證實 模糊觀測狀態回饋轉換控制方法。
第一章 簡介
實際上的應用，動態非線性系統一般都是存在時變參數或結構，因此控制器的設計是困難的去處理，尤其是在干擾不知道或者存在不確定的因素之下。所以我們利用以下要點來對付動態非線性系統。
1. 結合多模組轉換方法和模糊建模系統來對付隨機非線性時變系統。
2. 模糊輸出回授控制和模糊轉換建模系統被提供去對付非線性時變隨機系統穩定度的問題。
3. 利用 模糊觀測狀態回饋轉換控制最小化估測誤差。
第二章 系統模型與架構
本章主要介紹隨機非線性轉換系統與以模糊理論和likelihood function為基礎的架構，這些數學模型可以讓大家知道如何得到一個整合量測信號。而以模糊理論和likelihood function為基礎的架構可以知道演算彼此之間關係，此章分成下列兩個部分來介紹：
A. 系統模型
B. 估測誤差模型建構
最後得到系統模式與以模糊理論和likelihood function為基礎的架構將在下一章被使用。
第三章 穩定度分析
本章主要分析我們所建立模型的穩定度，為了使估測誤差在穩定狀態下估測誤差是否能趨近於0。
第四章 模糊觀測狀態回饋轉換控制設計
本章主要介紹以模糊理論和likelihood function為基礎的演算法如何運用數學推導找出影響精切度的參數。此章包含五個部分來介紹：
A. Hinf 模糊轉換控制器設計
B. H2 模糊轉換控制器設計
C. H2/Hinf模糊轉換控制器設計
D. 估測誤差值最小化設計
E. Likelihood function演算法
這將可使我們知道誤差大小及找出影響我們提出方法的干擾源及複雜度。
第五章 模擬結果
在此章節中，我們提出以模糊理論和likelihood function為基礎的演算法，去對付一些隨機非線性時變系統，去探討方法的可行性。
第六章 討論
在此篇論文研究中，我們提出以模糊理論和likelihood function為基礎的演算法。這將是一個很堅韌性方法，將來可運用在實際控制系統來對付隨機非線性時變系統中估測問題。

In this study, the problem of robust control for nonlinear stochastic systems subject to time-varying parameter is treated by a proposed switching fuzzy stabilization scheme via output feedback. Switching multiple-modeling approach has been used to deal with linear systems with time-varying parameters or structure. Conventionally, Takagi-Sugeno (TS) fuzzy modeling method is usually adopted to approximate the nonlinear time-invariant systems, but not suitable for nonlinear time-varying systems. Combining the switching multiple-modeling approach and TS fuzzy modeling method, a robust fuzzy observer-based controller, based on the switching TS fuzzy model, is proposed for the stabilization of the nonlinear time-varying stochastic systems. In order to mitigate the model approximation error and external disturbance in the systems, the proposed H2/Hinf switching fuzzy observer-based control achieves H2 suboptimal control and Hinf attenuation of external disturbance simultaneously. The conditions for the existence of the proposed H2/Hinf switching fuzzy observer-based controller are provided in terms of linear matrix inequalities (LMIs), allowing the use of standard convex optimization procedures to solve the proposed robust H2/Hinf output control design problem for nonlinear time-varying stochastic systems. Finally, numerical simulations are provided to illustrate the design procedure and to confirm the performance of the proposed robust H2/Hinf switching fuzzy observer-based controller for nonlinear time-varying stochastic systems.

1 Introduction 2 Switching Fuzzy Model for Nonlinear Time-Varying Stochastic Systems A. Switching Takagi-Sugeno Fuzzy Model for Nonlinear Time- Varying stochastic Systems
B. Estimation Error analysis of switching Fuzzy observer
3 StabilityAnalysis
4 The Mixed J2/Hinf Switching Fuzzy Observer-Based
Controller Design
A. The Hinf Switching Fuzzy Observer-based Controller
Design
B.The H2/Hinf Switching Fuzzy Mixed controller Design C. Calculation of the Covariance Matrix Q(k) for
weightings
6 Simulation Examples
7 Conclusions Bibliography

[1] H. K. Lam, F. H. F. Leung, and Y. S. Lee, “Design of a switching controller for nonlinear systems with unknown parameters based on a fuzzy logic approach,” IEEE Trans. System, Man, Cybern.---Part B: Cybern., vol. 34, no. 2, pp. 1068-1074, Apr. 2004.
[2] H. K. Lam, and F. H. F. Leung, “Fuzzy combination of fuzzy and switching state-feedback controllers for nonlienar systems subject toparameter uncertainties,” IEEE Trans. System, Man, Cybern.---Part B: Cybern., vol. 35, no. 2, pp. 269-281, Apr. 2004.
[3] H. Ohtake, K. Tanaka, and H. O. Wang, “Switching fuzzy control for nonlienar systems,” Intern. Symp. Intelligent Control, pp. 281-286, 2003.
[4] A. Isidori and A. Asolfi, “Disturbance attenuation and control via measurement feedback in nonlinear systems,” IEEE Trans. Automat. Contr., vol. 37, pp. 1283-1293, Sept. 1992.
[5] C. Scherer, “Mixed control,” in Trends in Control, A Euripean Perspective, A. Isidori Ed.. Berlin, Germany: Springer-Verlag, 1995, pp. 173-216.
[6] B.-S. Chen, C.-S. Tseng and H.-J. Uang, “Mixed fuzzy output feedback control design for nonlinear dynamix systems: An LMI approach,” IEEE Trans. Fuzzy Systems, vol. 8, no. 3, pp. 249--265, June 2000.
[7] H. A. P. Blom and Y. Bar-Shalon, “The interacting multiple model algorithm for systems with Markovian switching coefficients,” IEEE Trans. Automat. Contr., vol. 33, no. 8, pp. 780-783, Aug. 1988.
[8] K. A. Barbosa and C. E. de Souza, “Robust filtering for discrete-time uncertain linear systems using parameter-dependent Lyapunov functions,” Proc. American Contr. Conf. , vol. 4, pp. 3224-3229, 2002.
[9] K. A. Barbosa, A. Trofino, and C. E. de Souza, “Robust filtering for linear discrete-time state-space models with uncertain time-varying parameters” Proc. IEEE Intern. Conf. Acoust., Speech, Signal Processing, ICASSP, vol. 2, pp. 1389-1392, 2002.
[10] J. C. Geromel, J. Bernussou, G. Garcia and M. C. E. de Oliveira, “ and robust filtering for discrete-time linear systems,” SIAM Journ. Contr. Optim., vol. 38, no. 5, pp. 1353-1368, 2000.
[11] T. Takagi and M. Sugeno, “Fuzzy identification of systems and its application to modeling and control,” IEEE Trans. System, Man, Cybern., vol. 15, pp. 116-132, 1985.
[12] E. Kim, S. Ji and M. Park, “A new approach to fuzzy modeling,” IEEE Trans. Fuzzy Systems, vol. 5, no. 3, pp. 328-337, Aug. 1997.
[13] C. C. Wang and C. C. Chen, “A clustering-based method for fuzzy modeling,” IEICE Trans. Inf. & Syst., vol. E82-D, no. 6, pp. 1058-1065, 1999.
[14] M. Sugeno and T. Yasukawa, “A fuzzy-logic-based approach to qualitative modeling,” IEEE Trans. Fuzzy Systems, vol. 1, no. 1, pp. 7-31, Feb. 1993.
[15] C.-S. Tseng, and B.-S. Chen, “ fuzzy estimation for a class of nonlinear discrete-time dynamic systems,” IEEE Trans. Signal Processing, vol. 49, no. 11, pp. 2605-2619, Nov. 2001.
[16] X. Shen and L. Deng, “A dynamic system approach to speech enhancement using the filtering algorithm” IEEE Trans. Speech & Audio Processing, vol. 7, no. 4, pp. 391-399, Jul. 1999.
[17] N. Berman and U. Shaked, “ nonlinear filtering,” International Journal of Robust and Nonlinear Control, vol. 6, pp. 281-296, 1996.
[18] J. B. Burl, “ estimation for nonlinear systems,” IEEE Signal Processing Letts., vol. 5, no. 8, Aug. 1998.
[19] L. Xie, C. E. de Souza, and Y. Wang, “Robust filtering for a class of discrete-time uncertain nonlinear systems: An approach,” Intern. J. Robust & Nonlinear Contr., vol. 6, pp. 297-312, 1996.
[20] B.-S. Chen, C.-L. Tsai and Y.-F. Chen, “Mixed filtering design in multirate transmultiplexer systems: LMI approach,” IEEE Trans. Signal Processing, vol. 49, no. 11, pp. 2693-2701, Nov. 2001.
[21] B.-S. Chen, C.-L. Tsai and D.-S. Chen, “Robust and mixed filters for equalization designs of nonlinear Communications systems: Fuzzy interpolation approach,” IEEE Trans. Fuzzy Systems, vol. 11, no. 3, pp. 384--398, June 2003.
[22] Z. Tan, Y. C. Soh, and L. Xie, “Envelope-constrained filter design: An LMI optimization approach,” IEEE Trans. Signal Processing, vol. 48, no. 10, pp. 2960-2963, Oct. 2000.
[23] L. Xie, L. Lu, D. Zhang, and H. Zhang, “ deconvolution filtering of 2-d digital systems,” IEEE Trans. Signal Processing, vol. 50, no. 9, pp. 2319-2332, Sep. 2002.
[24] H. Zhou, L. Xie, and C. Zhang, “A direct approach to optimal deconvolution of periodic digital channels,” IEEE Trans. Signal Processing, vol. 50, no. 7, pp. 1685-1698, July 2002.
[25] R. T. Bambang, E. Shimemura and K. Uchida, “An algorithm for mixed robust controllers that satisfy variance constraints,” IEEE Conf. Contr. Application, vol. 1, pp. 281-286, 1992.
[26] P. P. Khargonekar and M. A. Rotea, “Mixed control: a convex optimization approach,” IEEE Trans. Automat. Contr., vol. 36, no. 7, pp. 824-837, July 1991.
[27] P. P. Khargonekar and M. A. Rotea, “Mixed filtering,” Proc. IEEE Conf. Decision & Contr., vol. 2, pp. 2299-2304, 1992.
[28] J. C. Geromel, P. L. D. Peres and S. R. Sonza, “Mixed control for continuous-time linear systems,” Proc. IEEE Conf. Decision & Contr., vol. 4, pp. 3717-3722, 1992.
[29] S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control theory, SIAM, Philadelphia, 1994.
[30] P. Gahinet, A. Nemiroski, A. J. Laub, and M. Chilali, LMI Control Toolbox, Natick, MA: Math Works, 1995.
[31] B.-S. Chen, B.-K. Lee and L.-B. Guo, “Optimal tracking design for stochastic fuzzy systems,” IEEE Trans. Fussy Systems, vol. 11, no. 6, pp. 796-813, Dec. 2003.
[32] M. J. Grimble and A. E. Sayed, “Solution of the optimal linear filtering problem for discrete-time systems,” IEEE Trans. Acoust., Speech, Signal Processing, vol. 38, pp. 1092-1104, July 1990.
[33] M.C. de Oliveira and J.C. Geromel, “A class of robust stability conditions where linear parameter dependence of the Lyapunov function is a necessary condition for arbitrary parameter dependence,” Systems & Control Letts., vol. 54, pp. 1131-1134, 2005.
[34] J. Daafouz and J. Bernussou, “Parameter dependent Lyapunov functions for discrete time systems with time varying parametric uncertainties,” Systems & Control Letts., vol. 43, pp. 355-359, 2001.
[35] D.C.W. Ramos and P.L.D. Peres, “A less conservative LMI condition for the robust stability of discrete-time uncertain systems,” Systems & Control Letts., vol. 43, pp. 371–378, 2001.