臺灣博碩士論文加值系統

本論文是以模糊類神經網路（Fuzzy Neural Network）為基礎，提出一個調整歸屬函數的新方法。我們首先介紹模糊類神經網路，此網路具有模糊邏輯及神經網路的特性。第二部份證明高斯函數可以由數個標準差較小的其他高斯函數所組成。第三部份為修改模糊類神經網路的歸屬函數成為五層模糊類神經網路（FNN5）。第四部份利用五層模糊類神經網路去近似幾個函數並證明五層模糊類神經網路是一個廣泛近似器。最後，我們將這個方法應用到調整比例積分（PI）控制器。我們經過模擬後，發覺模糊類神經網路與五層模糊類神經網路在精確度的要求上，都有很良好的模擬結果，但是五層模糊類神經網路在微調時，比模糊類神經網路更具有精確的效果。

In this thesis, a new method to tune the membership functions of fuzzy neural network (FNN) is presented. First we study the FNN it inherits the property of both fuzzy inference system and neural network. Then we present that any gaussian function can be represented by the linear combination of gaussian functions with small standard deviation. Therefore, it can be substituted for the second layer of FNN (called FNN5). We use the FNN5 to approximate some functions and prove that it is a universal approximator. Furthermore, apply this proposed method to tune PI controller based on gain phase margin (GPM) specifications. Both FNN and FNN5 have high performance by the simulation verification, however FNN5 is more accurate than FNN on fine-tuning.

Abstract (Chinese)i
Abstract (English)ii
Acknowledgementsiii
Contentsiv
List of Figuresvi
List of Tablesviii
1 Introduction1
2 Fuzzy Neural Network4
2.1 Fuzzy Inference System and Neural Network4
2.2 Structure of the FNN7
2.3 Basic Nodes Operation9
2.4 Supervised Gradient Descent Learning12
3 Approximations by Using Gaussian Functions16
3.1 Universal Approximation Theorem17
3.2 Examples22
3.3 Composition of the Membership Functions of FNN25
4 Additive Gaussian Membership Function in Fuzzy Neural Network26
4.1 Structure of the FNN527
4.2 Layer Operation of the FNN529
4.3 Supervised Learning32
4.4 Initialization34
4.5 Convergence36
5 Simulation Results39
5.1 Example 1：39
5.2 Example 2：43
5.3 Example 3：47
5.4 Example 4：52
6 Conclusion57
Bibliography58

[1] Y. C. Chen and C. C. Teng, "A Model Reference Control Structure Using a Fuzzy Neural Network," Fuzzy Sets and Systems. Vol. 73, pp. 291-312, 1995.
[2] Y. C. Chen and C. C. Teng, "Fuzzy Neural Network Systems in Model Reference Control Systems," in Neural Network System, Technique and Applications, Volume 6, Edited by C. T. Leondes, Academic Press, Inc. pp. 285-313, 1998.
[3] R. Hecht-Nielsen, "Theory of the Backup-Propagation Neural Network," Proc. Of the IEEE IJCNN, Vol. 1, pp. 593-605, 1989.
[4] R. Hecht-Nielsen, Neuralcomputing, Addison-Wesley, 1990.
[5] W. K. Ho, C. C. Hang and L. S. Cao, Tuning of PID controllers based on gain and phase margin specification, Automatica, pp. 497-502,1995.
[6] W. K. Ho and W. Xu, PID tuning for unstable processes based on gain and phase-margin specifications, IEE Proc.-Control Theory and Applications, 145 (1998) 392-396.
[7] S. Horikawa, T. Furuhashi, and Y. Uchikawa, "On Fuzzy Modeling Using Fuzzy Neural Networks with the Back-Propagation Algorithm," IEEE Trans. on Neural Networks, vol. 3, no. 5, pp. 801-806, 1992.
[8] J. S. Jang, "ANFIS: Adaptive-Network-Based fuzzy inference system," IEEE Trans. Sys. Man Cybern., vol. 23, no. 3, pp. 665-684, May/June 1993.
[9] M. I. Jordan and D.E. Rumelhart, "Forward models: supervised learning with a distal teacher," Submitted, pp. 1-49, 1991.
[10] C. C. Jou, "On the Mapping Capablity of Fuzzy Inference System," Proc. Int. Joint. Conf. On Neural Networks, Baltimore, ML II, pp. 708-713, 1992.
[11] L. V. Kantorovich and G. P. Akilov, Functional Analysis, 2nd ed. Oxford: Pergamon,1982.
[12] C. C. Ku and K. Y. Lee, "Diagonal Recurrent Neural Networks for Dynamic Systems Control," IEEE Trans. on Neural Networks, Vol. 6, No. 1, pp. 144-156, 1995.
[13] C. H. Lee and C. C. Teng, "Control of Nonlinear Systems Using Fuzzy Neural Networks," Proc. Asian Fuzzy Systems Symposium, Kenting, Taiwan, pp. 49-54, 1996.
[14] C. H. Lee and C. C.Teng, "A Novel Method for Stabilizing Nonlinear Nonminimum Phase Systems," submitted to IEEE Trans on Systems, Man, and Cybernetics-Part B: Cybernetics, 1998.
[15] C. T. Lin and C. S. G. Lee, Neural Fuzzy Systems, Prentice Hall: Englewood Cliff, 1996.
[16] C. T. Lin and C. S. G. Lee, Neural-Network-Based Fuzzy Logic Control and Decision
System, IEEE Trans. Computers 40(12), pp. 1320-1336, 1991., 1998.
[17] L. Ljung and T. Soderstrom, Theory and Practice of Recursive Identification. Cambridge, MA: M.I.T. Press, 1985.
[18] C. W. Ma and C. C. Teng, "Tracking a Near-field Moving Target Using Fuzzy Neural Networks," Fuzzy Sets and Systems (Accepted),1998.
[19] C. W. Ma and C. C. Teng, "A Fuzzy Neural Network Approach for 2-D Direction Finding in Multipath Environments," IEE Proceedings Radar, Sonar and Navigation (Accepted), 1998.
[20] H.L. Royden, Real Analysis, 2nd ed. New York:Macmillan, 1968.
[21] W. Rudin, Principles of Mathematical Analysis, 3rd edition, McGraw-Hill: New York,1976.
[22] D. E. Rumelhart and J. L. McClelland (eds.), Parallel Distributed Processing, Vol. I, M. I. T. Press, Cambridge, MA, 1986.
[23] 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 Transcations on Systems, Man and Cybernetics, vol. 25, no. 5, May, 1995.
[24] L. X. Wang, Adaptive Fuzzy Systems and Control: Design And Stability Analysis, Prentice Hall, 1994.
[25] P. J. Werbos, "Back Propagation Through Time: What it does and how to do it," Proc. Of the IEEE, Vol. 78, No. 10, pp. 1550-1560,1990.
[26] X. J. Zeng and M.G. Singh, "A relationship Between Membership Functions and Approximation Accuracy in Fuzzy Systems," IEEE Trans. on Systems,Man, and cybernetics-Part B: Cybernetics, Vol. 26, No.1, pp.176-180,1996.