簡易檢索 / 詳目顯示

研究生: 陳銘滄
Ming-Chang Chen
論文名稱: 即時適應性階層式T-S模糊神經控制器的設計與應用
Design and Applications of On-Line Adaptive Hierarchical T-S Fuzzy-Neural Controller
指導教授: 蘇順豐
Shun-Feng Su
王偉彥
Wei-Yen Wang
口試委員: 李祖添
Tsu-Tian Lee
王文俊
Wen-June Wang
陶金旺
C.W. Tao
鄭錦聰
Jin-Tsong Jeng
郭重顯
Chung-Hsien Kuo
陳松雄
Song-Shyong Chen
學位類別: 博士
Doctor
系所名稱: 電資學院 - 電機工程系
Department of Electrical Engineering
論文出版年: 2011
畢業學年度: 99
語文別: 英文
論文頁數: 96
中文關鍵詞: T-S 模糊神經控制器
外文關鍵詞: T-S Fuzzy-Neural Controller
相關次數: 點閱:221下載:7
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 本論文提出一種新穎的控制方法,為即時適應T-S模糊類神經模型,並透過此方法去鑑別未知的動態系統。其中,強健控制器是設計用來補償模型誤差和外界干擾。由於大部分的系統都是非線性,因此本論文使用均值定理,將一個非線性系統轉至為虛擬線性系統,然後T-S模糊類神經模型便能近似這些未知的動態系統。在一個未知系統中,T-S模糊神經網絡模型是一種有效的鑑別方法。但是T-S模糊神經模型在處理一個高階系統時,由於模糊規則數過於龐大,將耗費大量運算時間。因此,我們提出一種層次的架構,將複雜的模糊類神經網路架構,分成數個低階的子系統,以降低模糊規則數與減少運算時間。最後,本文舉出一些affine非線性系統的例子,由模擬結果可以證明,該控制器的設計呈現良好的性能和效果。


    This dissertation proposes a novel control method for identification of a class of uncertain systems by using on-line adaptive T-S fuzzy-neural modeling. And the robust controller is designed to compensator modeling errors and external disturbances. This dissertation uses the mean value theorem to transform the nonlinear system dynamic into a virtual linear system because the most systems are nonlinear. Then the T-S fuzzy-neural model can identify the dynamic model of the linearized system. Although T-S fuzzy-neural modeling is an efficient identification method for uncertain systems, it encounters serious problem of fuzzy rules explosion in processing a high dimensional system. Furthermore, this problem leads to large computing time. Therefore, we propose a kind of hierarchical structure through which the complex structure of fuzzy-neural networks can be modeled by using a family of subsystems with fewer dimensions. By this hierarchical structure, the fuzzy rules and the computation time will decrease. Finally, this dissertation gives some examples for affine nonlinear systems, and the simulation results illustrate that the proposed controller design presents good performances and effectiveness.

    ABSTRACT (In Chinese)---I ABSTRACT (In English)---II CONTENTS---III LIST OF FIGURES---V LIST OF TABLES---VII Chapter 1 Introduction---1 1.1 Motivations---1 1.2 Contribution---4 1.3 Organization of the Dissertation---5 Chapter 2 T-S Fuzzy Neural Model with Hierarchical Structure---7 2.1 Fuzzy Control System---7 2.1.1 Fuzzifier---7 2.1.2 Fuzzy Rule Base---9 2.1.3 Inference Engine---9 2.1.4 Deffuzzifiers---9 2.2 T-S Fuzzy Model---11 2.3 T-S Fuzzy-Neural Model---12 2.4 Hierarchical T-S Fuzzy Neural Model---14 2.4.1 Description of the Hierarchical-FNNs---16 Chapter 3 Robust T–S Fuzzy-Neural Control System and Its Application---21 3.1 Problem Formulation---21 3.1.1 T-S Fuzzy-Neural Model---23 3.1.2 Controller Design for On-line Modeling and Robust Tracking---25 3.2 Simulation Results---31 Chapter 4 Hierarchical T-S Fuzzy-Neural Control System and Its Application---46 4.1. Problem Formulation---46 4.2 Design of Hierarchical T-S Fuzzy-Neural Controller---47 4.3 Simulation Results---54 Chapter 5 Conclusions---66 5.1 Conclusions---66 5.2 Suggestions for Further Research---67 References---68 Appendix---78 Biography and Publication---83

    [1] W.-Y. Wang, M.-L. Chan, C.-C. Hsu, and T.-T. Lee, “H-inf. Tracking-Based Sliding Mode Control for Uncertain Nonlinear Systems via an Adaptive Fuzzy-Neural Approach,” IEEE Transactions on Systems, Man, And Cybernetics-Part B, vol. 32, no. 4, pp. 483-492, Aug. 2002.
    [2] H. D. Tuan, P. Apkarian, T. Narikiyo, and Y. Yamamoto, “Parameterized Linear Matrix Inequality Techniques in Fuzzy Control System Design,” IEEE Transactions on Fuzzy Systems, vol. 9, pp. 324-332, April 2001.
    [3] Y.-G. Leu, W.-Y. Wang, and I-H. Li “RGA-based On-Line Tuning of BMF Fuzzy-Neural Networks for Adaptive Control of Uncertain Nonlinear Systems,” Neurocomputing, vol. 72, no. 10-12, pp. 2636-2642, June 2009.
    [4] J.-L. Wu, W.-Y. Wang, and T.-T. Lee, “Robust H-inf Output Feedback Control for Discrete-Time Nonaffine Nonlinear Systems with Structured Uncertainties,” International Mathematical Forum-Journal for Theory and Applications, vol. 1, no. 25-28, pp. 1297-1312, 2006.
    [5] C.-W. Tao, W.-Y. Wang, and M.-L. Chan, “Design of Sliding Mode Controllers for Bilinear Systems with Time Varying Uncertainties,” IEEE Transactions on Systems, Man, And Cybernetics-Part B, vol. 34, no. 1, pp. 639-645, Feb. 2004.
    [6] W.-Y. Wang, C.-Y. Cheng, and Y.-G. Leu, “An Online GA-Based Output-Feedback Direct Adaptive Fuzzy-Neural Controller for Uncertain Nonlinear Systems,” IEEE Transactions on Systems, Man, And Cybernetics-Part B, vol. 34, no. 1, pp. 334-345, Feb. 2004.
    [7] J. Yu, K. Zhang, and S. Fei, “ Adaptive Fuzzy Tracking Control of a Class of Stochastic Nonlinear Systems with Unknown Dead-Zone Input,” International Journal of Fuzzy Systems, vol. 10, no. 1, March 2008.
    [8]C.-S. Ting, “A Robust Fuzzy Control Approach to Stabilization of Nonlinear Time-delay Systems with Saturating Inputs,” International Journal of Fuzzy Systems, vol. 10, no. 1, March 2008.
    [9]C.-Y. Kuo and H.-F. Wang, “Overview of Fuzzified Neural Networks with Comparison of Learning Mechanism,” International Journal of Fuzzy Systems, vol. 10, no. 2, June 2008.
    [10] C.-C. Hsu and W.-Y. Wang, “Discrete Modeling of Uncertain Continuous Systems Having an Interval Structure Using Higher-Order Integrators,” International Journal of Systems Science, vol. 31, no. 4, pp. 467-477, 2000.
    [11] H.-O. Wang, K. Tanaka, and M. F. Griffin, “An Approach to Fuzzy Control of Nonlinear Systems: Stability and Design Issues,” IEEE Transactions on Fuzzy Systems, vol. 4, pp. 14-23, Feb. 1996.
    [12] Y.-G. Leu, W.-Y. Wang, and T.-T. Lee, “Robust Adaptive Fuzzy-Neural Controllers for Uncertain Nonlinear Systems,” IEEE Transactions on Robotics and Automation, vol. 15, no. 5, pp. 805-817, Oct. 1999.
    [13] W.-Y. Wang, Y.-H. Chien, and I-H. Li, “An On-Line Robust and Adaptive T-S Fuzzy-Neural Controller for More General Unknown Systems,” International Journal of Fuzzy Systems, vol. 10, no. 1, pp. 33-43, 2008.
    [14] Rigling, B. D. and Moses, R. L., “Taylor Expansion of the Differential Range for Monostatic SAR,” IEEE Transactions on aerospace and electronic system, vol. 41, no. 1, January 2005.
    [15] S. I. Grossman and W. R. Derrick, Advanced Engineering Mathematics, Happer & Row, 1998.
    [16] K. Hornik, M. Stinchcombe, and H. White, “Multilayer Feedforward Networks are Universal Approximators,” Neural Networks, no. 2, pp. 359-366, 1989.
    [17] L.-X. Wang and J. M. Mendel, “Fuzzy Basis Functions, Universal Approximation, and Orthogonal Least Squares Learning,” IEEE Transactions on Neural Networks, vol. 3, no. 5, pp. 807-814, 1992.
    [18] C.-H. Wang, W.-Y. Wang, T.-T. Lee, and P.-S. Tseng, “Fuzzy B-Spline Membership Function (BMF) and Its Applications in Fuzzy-Neural Control,” IEEE Transactions on Systems Man and Cybernetics, vol. 25, no. 5, pp. 841-851, May 1995.
    [19] C.-L. Hwang, and L.-J. Chang, “Fuzzy Neural-Based Control for Nonlinear Time-Varying Delay Systems,” IEEE Transactions on System Man and Cybernetics-Part B, vol. 37, no. 6, pp. 1471-1485, 2007.
    [20] C.-F. Hsu, C.-M. Lin, and T.-T. Lee, “Wavelet Adaptive Backstepping Control for a Class of Nonlinear Systems,” IEEE Transactions on Neural Networks, vol. 17, no. 5, pp. 1175-1183, Sept. 2006.
    [21] L.-X. Wang, Adaptive Fuzzy Systems and Control, Prentice Hall International, 1994.
    [22] X. Liu, and Q. Zhang, “Approaches to Quadratic Stability Conditions and H-inf Control Sesigns for T-S Fuzzy Systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 6, pp. 830-839, 2003.
    [23] C.-S. Chen, “Adaptive Fuzzy Control of Uncertain Multivariable Nonlinear Systems,” Ph.D. dissertation, National Taiwan University, Taipei, Taiwan, 2002.
    [24]T. Takagi and M. Sugeno, “Fuzzy Identification of Systems and Its Application to Modeling and Control,” IEEE Transactions on Systems, Man and Cybernetics, vol. 15, pp. 116-132, Jan. 1985.
    [25] G. Feng, S. G. Cao, N.W. Rees, and C. K. Chak, “Design of Fuzzy Control Systems with Guaranteed Stability,” Fuzzy Sets Systems, vol. 85, pp. 1-10, 1997.
    [26] S. G. Cao, N.W. Rees, and G. Feng, “Stability Analysis and Design for a Class of Continuous-Time Fuzzy Control Systems,” Int. J. Control, vol. 64, no. 6, pp. 1069-1087, 1996.
    [27] G. S. Cao, N.W. Rees, and G. Feng, “Analysis and Design for a Class of Complex Control Systems: Parts I and II,” Automatica, vol. 33, no. 6, pp. 1017-1028, 1997.
    [28]W.-Y. Wang, Y.-H. Chien, Y.-G. Leu, and T.-T. Lee, “Adaptive T-S Fuzzy-Neural Modeling and Control for General MIMO Unknown Nonaffine Nonlinear Systems Using Projection Update Laws,” Automatica, vol. 46, pp.852-863, 2010.
    [29] W.-Y. Wang, Y.-H. Chien, Y.-G. Leu, and T.-T. Lee, “On-line Adaptive T-S Fuzzy-Neural Control for a Class of General Multi-Link Robot Manipulators,” International Journal of Fuzzy Systems, vol. 10, no. 4, pp. 240-249, Dec. 2008.
    [30] W.-Y. Wang, I-H. Li, L.-C. Chien, and S.-F. Su, “On-line Modeling and Control via T-S Fuzzy Models for Nonaffine Nonlinear Systems Using a Second Type Adaptive Fuzzy Approach,” International Journal of Fuzzy Systems, vol. 9, no. 3, pp. 152-161, 2007.
    [31] C. W. Park, and Y. W. Cho, “T-S Model Based Indirect Adaptive Fuzzy Control Using Online Parameter Estimation,” IEEE Transactions on Systems, Man and Cybernetics- Part B, vol. 34, no. 6, pp. 2293-2302, 2004.
    [32] P. P. Kumar, I. Kar, and L. Behera, “Variable-Gain Controllers for Nonlinear Systems Using the T–S Fuzzy Model,” IEEE Transactions on Systems, Man and Cybernetics-Part B, vol. 36, no. 6, pp. 1442-1449, Dec. 2006.
    [33] C. Lin, Q.-G. Wang, and T.-H. Lee, “H∞ Output Tracking Control for Nonlinear Systems via T–S Fuzzy Model Approach,” IEEE Transactions on Systems, Man and Cybernetics-Part B, vol. 36, no. 2, pp. 450-457, April 2006.
    [34] M. C. Hwang and X. Hu, “A Robust Position/Force Learning Controller of Manipulators via Nonlinear H∞ Control and Neural Networks,” IEEE Transactions on Systems, Man and Cybernetics-Part B, vol. 30, no. 2, pp. 310-321, April 2000.
    [35] R. V. Monopoli, “Model Reference Adaptive Control with an Augmented Error Signal,” IEEE Transactions Automatic Control, vol. AC-19, no. 5, pp. 474-484, Oct. 1974.
    [36] Tong, S. and Y. Li, “Direct Adaptive Fuzzy Backstepping Control for a Class of Nonlinear Systems,” Int. J. Innovative Computing, Information and Control, vol.3, no.4, pp.887-896, 2007.
    [37] P. A. Ioannou and J. Sun. Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
    [38] S. S. Sastry and A. Isidori, “Adaptive Control of Linearizable Systems,” IEEE Transactions Autom. Control, vol. 34, no. 11, pp. 1123-1131, Nov. 1989.
    [39] S. Monaco and D. Normand-Cyrot, “Minimum-Phase Nonlinear Discrete-Time Systems and Feedback Stabilization,” in Proc. IEEE Conference Decision Control, Los Angeles, CA, 1987, pp. 979-986.
    [40] L.-X. Wang, “Stable Adaptive Fuzzy Control of Nonlinear Systems,” IEEE Transactions on Fuzzy System, vol. 1, no. 2, pp. 146-155, May 1993.
    [41] K. S. Narendra and A. M. Annaswamy, Stable Adaptive Systems, Englewood Cliffs, NJ: Prentice-Hall, 1989.
    [42] S. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness. Englewood Cliffs, NJ: Prentice-Hall, 1989.
    [43] C. K. Chak, G. Feng, and J. Ma, “An Adaptive Fuzzy Neural Network for MIMO System Model Approximation in High-Dimensional Spaces,” IEEE Transactions on Systems, Man and Cybernetics, vol. 28, no. 3, pp. 436-446, June 1998.
    [44] Y. Gao and M. Joo Er, “Online Adaptive Fuzzy Neural Identification and Control of a Class of MIMO Nonlinear Systems,” IEEE Transactions on Fuzzy Systems, vol. 11, no. 4, pp. 462-477, August 2003.
    [45] S.-J. Huang and R.-J. Lian, “A Hybrid Fuzzy Logic and Neural Network Algorithm for Robot Motion Control,” IEEE Transactions on Industrial Electronics, vol. 44, no. 3, June 1997.
    [46] K. Hiroaki et al., “Functional Completeness of Hierarchical Fuzzy Modeling,” Inf. Sci., vol. 110, no. 1-2, pp. 51-60, 1998.
    [47] G. V. Raju and J. Zhou, “Adaptive Hierarchical Fuzzy Controller,” IEEE Transactions Syst., Man, Cybern., vol. 23, no. 4, pp. 973-980, Aug. 1993.
    [48] M. Denna, G. Mauri, and A. M. Zanaboni, “Learning Fuzzy Rules with Tabu Search-an Application to Control,” IEEE Transactions Fuzzy Syst., vol. 7, no. 2, pp. 295–318, Apr. 1999.
    [49] L.-X.Wang, “Analysis and Design of Hierarchical Fuzzy Systems,” IEEE Transactions Fuzzy Syst., vol. 7, no. 5, pp. 617–624, Oct. 1999.
    [50]C.-F. Juang, C.-M. Hsiao, and C.-H. Hsu, “Hierarchical Cluster-Based Multispecies Particle-Swarm Optimization for Fuzzy-System Optimization,” IEEE Transactions on fuzzy systems, vol. 18, no. 1, February 2010.
    [51] K. Sun-Yuan et al., “Synergistic Modeling and Applications of Hierarchical Fuzzy Neural Networks,” Proc. IEEE, vol. 87, no. 9, pp. 1550–1574, Sep. 1999.
    [52] M. Brown, K. M. Bossley, D. J. Mills, and C. J. Harris, “High Dimensional Neurofuzzy Systems: Overcoming the Curse of Dimensionality,” in Proc. 4th Int. Conference Fuzzy Systems, pp. 2139–2146, 1995.
    [53] O. Huwendiek and W. Brockmann, “Function Approximation with Decomposed Fuzzy Systems,” Fuzzy Sets Syst., vol. 101, pp. 273–286, 1999.
    [54] Ronald R. YageI, “On a Hierarchical Structure for Fuzzy Modeling and Control,” IEEE Transactions on Systems, Man and Cybernetics, vol. 23, no. 4, July 1993.
    [55] K.-S. Tang, K.-F. Man, Z.-F. Liu, and Sam Kwong, “Minimal Fuzzy Memberships and Rules Using Hierarchical Genetic Algorithms,” IEEE Transactions on Industrial Electronics, vol. 45, no. 1, February 1998.
    [56] X.-J. Zeng and J. A. Keane, “Separable Approximation Property of Hierarchical Fuzzy Systems,” IEEE Conference on Fuzzy System, pp. 951-956, May 2005.
    [57] Z. G. Hou, M. M. Gupta, P. N. Nikiforuk, and M. Tan, and L. Cheng, “A Recurrent Neural Network for Hierarchical Control of Interconnected Dynamic Systems,” IEEE Transactions on Neural Networks, vol. 18, no. 2, pp.466-481, 2007.
    [58] R. J. Leduce, B. A. Brandin, M. Lawford, and W. M. Wonham, “Hierarchical Interface-Based Supervisory Control-Part I: serial case,” IEEE Transactions on Automatic Control, vol. 50, no. 9, September 2005.
    [59] C. Wei and L.-X. Wang, “A Note on Universal Approximation by Hierarchical Fuzzy Systems,” Inf. Sci., vol. 123, pp. 241–248, 2000.
    [60] X.-J. Zeng and J. A. Keane, “Approximation Capabilities of Hierarchical Fuzzy Systems,” IEEE Transactions on Fuzzy Systems, vol. 13, no. 5, October 2005.
    [61] H. Rainer, “Rule Generation for Hierarchical Fuzzy Systems,” in Proc. Annu. Conference North American Fuzzy Information Processing, 1997, pp. 444–449.
    [62] I-H. Li, W.-Y. Wang, S.-F. Su, and Y.-S. Lee, “A Merged Fuzzy Neural Network and Its Applications in Battery State-of-Charge Estimation,” IEEE Transactions on Energy Conversion, vol. 22, no. 3, pp. 697-708, 2007.
    [63] W.-Y. Wang, I-H. Li, M.-C. Chen, S.-F. Su, and Y.-G. Leu, “A New Time-Efficient Structure for Observer-Based Adaptive Fuzzy-Neural Controllers for Nonaffine Nonlinear Systems,” International Journal of Innovative Computing, Information and Control, vol. 6, no. 3, 2010.
    [64] W.-Y. Wang, I-H. Li, S.-C. Li, M.-S. Tsai, and S.-F. Su, “A Dynamic Hierarchical Fuzzy Neural Network for a General Continuous Function,” International Journal of Fuzzy Systems, vol. 11, no. 2, pp. 141-147, June 2009.
    [65] X.-J. Zeng and J. A. Keane, “Approximation Capabilities of Hierarchical Hybrid Systems,” IEEE Transactions on Systems, Man and Cybernetics, Part A, vol. 36, no. 5, pp. 1029-1039, September 2006.
    [66] Y.-S. Lee, W.-Y. Wang, and T.-Y. Kuo, “Soft Computing for Battery State-of-Charge (BSOC) Estimation in Battery String Systems,” IEEE Transactions on Industrial Electronics, vol. 55, no. 1, pp. 229-239, Jan. 2008.
    [67] B. Allotta, L. Pugi, and F. Bartolini, “Design and Experimental Results of an Active Suspension System for a High-Speed Pantograph,” ASME Dynamic Systems and Control Division, vo. 13, no. 5, pp. 548-557, Oct. 2008.
    [68] Y. Jin, D. Yu, and X. Song, “An Integrated-Error-Based Adaptive Neuron Control and Its Application to Vehicle Suspension Systems,” IEEE International Conference on Control and Automation, pp. 564-569, June 2007.
    [69]J. Cao, H. Liu, P. Li, and D. Brown, “Adaptive Fuzzy Logic Controller for Vehicle Active Suspensions with Interval Type-2 Fuzzy Membership Functions,” IEEE International Conference on Fuzzy Systems, pp. 83-89, June 2008.
    [70] J. Cao, H. Liu, P. Li, and D. J. Brown, “State of the Art in Vehicle Active Suspension Adaptive Control Systems Based on Intelligent Methodologies,” IEEE transactions on intelligent transportation systems, vol. 9, no. 3, Sep. 2008.
    [71] J. S. Lin and I. Kanellakopoulos, “Nonlinear Design of Active Suspensions,” IEEE Control Systems, vol. 17, no. 3, pp.45-59, June 1997.
    [72] Nurkan Yagiz, Yuksel Hacioglu, and Yener Taskin, “Fuzzy Sliding-Mode Control of Active Suspensions,” IEEE Transactions onindustial electronics, vol. 55, no. 11, Nov. 2008.
    [73] J.-S. Lin and W.-E. Ting, “Nonlinear Control Design of Anti-lock Braking Systems with Assistance of Active Suspension,” IET Control Theory Appl., vol. 1, vo. 1, Jan. 2007.
    [74] J. Shao, L. Zheng, Y. N. Li, J. S. Wei, and M. G. Luo, “The Integrated Control of Anti-lock Braking System and Active Suspension in Vehicle,” Fourth International Conference on Fuzzy Systems and Knowledge Discovery, vol. 4, pp. 519-523, Aug. 2007.
    [75] S. Lou, Z. Fu, L. Zhang, and C. Xu, “Integrated Control of Semi of Semi-Active Suspension and ABS Based on Sliding Mode Theory,” Control Conference, pp. 3214-3218, Jul. 2010, Beijing, China.
    [76]A. Alleyne, “Improved Vehicle Performance Using Combined Suspension and Braking Forces,” American Control Conference, vol. 3, pp. 1672-1676, Jun. 1995.
    [77] W. Y. Wang, I-H. Li, M. C. Chen, S. F. Su, and S. B. Hsu, “Dynamic Slip Ratio Estimation and Control of Antilock Braking Systems using an Observer-Based Direct Adaptive Fuzzy-Neural Controller,” IEEE Transactions on Industrial Electronics, vol. 56, no. 5, pp. 1746-1756 , 2008.
    [78] C. Canudas-De-Wit, P. Tsiotras, E. Velenis, M. Basset, and G. Gissinger, “Dynamic Friction Models for Road/Tire Longitudinal Interaction,” Vehicle System Dynamics, pp. 1-23, Oct. 14, 2002.
    [79] G. F. Mauer, “A Fuzzy Logic Controller for an ABS Braking System,” IEEE Transactions on Fuzzy Syst., vol. 3, no. 4, Nov. 1995.
    [80] Y. Lee and S. H. Zak, “Genetic Neural Fuzzy Control of Anti-Lock Brake Systems,” Proceedings of the American Control Conference, Arlington VA, Jun. 25-27, 2001.
    [81] C.-M. Lin and C.-F. Hsu, “Neural-Network Hybrid Control for Antilock Braking Systems,” Transactions on Neural Networks, vol. 14, no. 2, Mar. 2003.
    [82] B. Breuler, U. Eichhorn, and J. Roth, “Measurement of Tyre/Road Friction Ahead of the Car and Inside the tyre,” in Proc.92 Int. Symp. Advanced Vehicle control (AVEC), pp. 347-353, 1999.
    [83] W.-Y. Wang, G.-M. Chen, and C.-W. Tao, “Stable Anti-Lock Braking System Using Output-Feedback Direct Fuzzy Neural Control,” IEEE International Conference Systems, Man and Cybernetics, pp. 3675-3680, Oct. 2003.
    [84] C.-T. Lin and C.-S. Lee, Neural Fuzzy Systems, Prentice Hall International, Inc, 1996.
    [85] M. Vidyasagar, Nonlinear Systems Analysis, Prentice-Hall, 1993.

    QR CODE