本論文研究主要是用來改善小腦模型控制器(cerebellar model articulation controller：CMAC)的學習效能，有效結合運用灰關連分析(grey relational Analysis)的特性，動態調整小腦模型之學習率與記憶單元內容更新兩者來獲得效能的提升，並進行相關應用實例的研究。
小腦模型控制器是一種採用監督式學習的類神經網路，具備快速的學習收斂速度、良好區域類化的能力、簡單的運算處理、容易以硬體實現等優點，常應用在智慧型控制、圖形辨識、信號處理、資料探勘和機器人等領域。在訓練學習階段，小腦模型控制器鄰近的記憶單元存在所謂學習干擾(learning interference)的現象，此現象會明顯影響小腦模型控制器的學習效能，因此，快速學習與準確收斂是小腦模型控制器研究領域最重要的兩個課題，此研究的困難點在於如何達到快速穩定學習與準確度兩者皆改善的效果並超越過去既有的方法，本論文的研究目的即為減少學習干擾的影響，並期能同時達到快速穩定學習與準確收斂兩者兼備的效能；本論文提出輸入狀態在目前訓練學習階段，考慮訓練的次數與其輸出誤差經由灰關連分析計算得出的灰關連係數(grey relational coefficient)，研究定義針對每個輸入狀態的動態調適灰學習率(grey learning rate)，以期獲得較穩定快速的學習效果；此外也提出一個新型可信度分配的機制，不僅考慮以記憶單元過去累積的學習次數，並結合目前訓練階段中記憶單元已經被訓練學習的輸入狀態比例，以及記憶單元中包含輸入狀態的灰關連級數(grey relational grade)關係來做為可信度分配的依據，以期達到快速準確收斂的學習效果。
本論文所提出的方法主要依據可信度分配(credit assignment)的機制與藉由動態調整的灰學習率來達成預期研究的目標，經由後續的模擬實驗結果與應用實例的驗證，本論文研究確實可有效提昇小腦模型控制器的學習速度與準確度，並順利應用於不同的領域中。

The main purpose of this thesis is to improve the learning performance of CMAC (Cerebellar Model Articulation Controller). Using grey relational analysis based approach, adaptively regulate both learning rate and updating memory cells to increase the performance of CMAC. Additionally, some applications of CMAC are also discussed in the thesis.
The advantages of supervised CMAC neural network are fast learning convergence, capable of mapping nonlinear functions quickly due to its local nature of weight updating, simple architecture, easily processing and hardware implementation. CMAC could be applied to intelligent control, pattern recognition, signal processing, data mining, robotics and other fields. In learning phase, the neighbor memory cells of CMAC have the phenomena of learning interference. The phenomena evidently reduce the learning performance of CMAC. Therefore, fast learning and accurate convergence are the two issues to be most concerned in the research area of CMAC. The difficulty of research in this field is to improve the trade-off between fast learning and accurate convergence over that of existing methods. In order to improve the learning speed and accuracy simultaneously, this thesis investigates to incorporate grey relational coefficients with number of training iterations to obtain an adaptive and appropriate grey learning rate for each input state to improve the CMAC stability and convergence. Additionally, this thesis also proposes that the amount of weight adjustment to a memory cell of an addressed memory cell must be relational to the trained input area, grey relational grade in the current training iteration and the inverse of the number of learning times to minimize the learning interference. A novel credit apportionment approach is thus derived for implementing this idea to achieve fast and accurate learning performance.
The results of the experiments and various applications conducted in this study clearly demonstrate that the proposed approach provides a more accurate learning mechanism and faster convergence. The proposed CMAC model with fast learning and accurate convergence can perform adequately in various applications.

參考文獻(References)
[1] J. S. Albus, “A New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC)”, ASME J. Dynamic Systems, Measurement, Control, pp.220-227, 1975.
[2] J. S. Albus, “Data Storage in the Cerebellar Model Articulation Controller (CMAC)”, ASME J. Dynamic Systems, Measurement, Control, pp.228-233, 1975.
[3] W. T. Miller, F. H. Glanz and L. G. Kraft, “CMAC: An Associative Neural Network Alternative to Backpropagation”, Proceedings of the IEEE , vol.78 , no.10 , pp.1561 – 1567, 1990.
[4] D. E. Thompson and S. Kwon, “Neighborhood Sequential and Random Training Techniques for CMAC”, IEEE Transaction on Neural Networks, vol.6, no.1, pp.196-202 1995.
[5] C. T. Chiang and C. S. Lin, “Integration of CMAC and Radial Basis Function Techniques”, IEEE International Conference on Systems, Man and Cybernetics, 'Intelligent Systems for the 21st Century', vol.4, pp. 3263-3268, 1995.
[6] C. T. Chiang and C. S. Lin, “CMAC with General Basis Functions”, Neural Networks, vol.9, no.7, pp.1199-1211, 1996.
[7] S. Sayil and K. Y. Lee, “A Hybrid Maximum Error Algorithm with Neighborhood Training for CMAC”, IEEE Proceedings of the International Joint Conference on Neural Networks, vol.1, pp.165-170, 2002.
[8] G. Horváth and T. Szabó, “CMAC Neural Network with Improve Generalization Property for System Modeling”, IEEE Instrumentation and Measurement Technology Conference, vol.2, pp.1603-1608, 2002.
[9] M. F. Yeh and H. C. Lu, “On-Line Adaptive Quantization Input Space in CMAC Neural Network”, IEEE International Conference on Systems, Man and Cybernetics, vol.4, 2002.
[10]Hung –Ching Lu, Ming- Feng Yeh and Jui-Chi Chang, “CMAC Study with Adaptive Quantization”, IEEE International Conference on Systems, Man and Cybernetics, October 8-11, 2006, Taipei, Taiwan.
[11]S. D. Teddy, E. M.-K. Lai, and C. Quek, “Hierarchically Clustered Adaptive Quantization CMAC and Its Learning Convergence”, IEEE Transaction on Neural Networks, vol.18, no.6, pp.1658-1681, November 2007.
[12]H. M. Lee and C. M. Chen, “Self-Organizing HCMAC Neural-Network Classifier”, IEEE Transaction on Neural Networks, vol.14, no.1, pp.15-27, 2003.
[13]J. C. Jan and S. L. Hung, “High-order MS_CMAC Neural Network”, IEEE Transaction on Neural Networks, vol.12, no.3, pp.598-603, 2001.
[14]J. S. Ker, Y. H. Kuo, R. C. Wen and B. D. Liu, “Hardware Implementation of CMAC Neural Network with Reduce Storage Requirement”, IEEE Transaction on Neural Networks, vol.8, no.6, pp.1545-1556, 1997.
[15]C. S. Lin and C. T. Chiang, “Learning Convergence of CMAC Technique”, IEEE Transaction on Neural Networks, vol.8, no.6, pp.1281-1292, 1997.
[16]R. Smalz and M. Conrad, “Combining Evolution with Credit Apportionment: A New Learning Algorithm for Neural Nets”, Neural Networks, vol.7, no.2, pp.341-351, 1994.
[17]V. L. Plantamura, B. Soucek, and G. Visaggio, “Holographic Fuzzy Learning for Credit scoring”, Proceeding of the International Joint Conference on Neural Networks, vol.1, pp.729-732, 1993.
[18]Ming-Feng Yeh and Kuang-Chiung Chang, “A Self-Organizing CMAC Network With Grey Credit Assignment”, IEEE Transaction on System, Man, and Cybernetics-Part B: Cybernetics, vol.36, no.3, pp.623-635, 2006.
[19]Luis Weruaga and Barbara Kieslinger, “Tikhonov Training of the CMAC Neural Network”, IEEE Transaction on Neural Networks, vol.17, no.3, pp.613-622, 2006.
[20]S. F. Su, T. Tao, and T. H. Hung, “Credit Assigned CMAC and Its Application to Online Learning Robust Controllers”, IEEE Transaction on System, Man, and Cybernetics-Part B: Cybernetics, vol.33, no.2, pp.202-213, 2003.
[21]H. C. Lu and J. C. Chang, “Enhance the Performance of CMAC Neural Network via Fuzzy Theory and Credit Apportionment”, IEEE Proceedings of the 2002 International Joint Conference on Neural Networks, vol.1, pp.715-720, 2002.
[22]Shun-Feng Su, Zne-Jung Lee, and Yan-Ping Wang, “Robust and Fast Learning for Fuzzy Cerebellar Model Articulation Controllers”, IEEE Transaction on System, Man, and Cybernetics-Part B: Cybernetics, vol.36, no.1, pp.203-208, 2006.
[23]Po- Lun Chang, Ying- Kuei Yang and Horng- Lin Shieh, “A Novel Learning Framework of CMAC Via Grey-area-time Credit Apportionment and Grey Learning Rate”, Proceedings of the Seventh International Conference on Machine Learning and Cybernetics(ICMLC), Kunming, China, 12-15 July 2008, Volume 6 of 7, pp. 3096-3101.
[24]J. S. Albus, ”A Model of the Brain for Robot Control, Part2: A Neurological Model”, BYTE, vol.4, no.7, pp.54-95,1979.
[25]Y. Iiguni, “Hierarchical Image Coding via Cerebellar Model Arithmetic Computers”, IEEE Transaction on Image Processing, vol.5, no.10, pp.1393-1401, 1996.
[26]A. Cichocki and R. Unbehauen, Neural Networks for Optimization and Signal Processing. New York : Wiley, 1993.
[27]M. Smith, Neural Networks for Statistical Modeling. New York: Van Nostrand Reinhold, 1993.
[28]M. F. Yeh, “Single-input CMAC Control System”, Neurocomputing, 70, pp.2638-2644, 2007.
[29]Ted Tao, Chao-Peng Wei, Liang-Yu Chen, “The Auxiliary CMAC Applied to Online Tuning Robust Fuzzy Controllers”, IEEE International Conference on Fuzzy Systems, pp.783-789, 2008.
[30]Po- Lun Chang, Ying- Kuei Yang, Horng- Lin Shieh, Fei-Hu Hsieh, Hen-Kung Wang, “Function Approximation Using Robust Fuzzy-GreyCMAC Method”, Proceedings of IEEE International Conference on Industrial Technology, ICIT 2009, AF016292, 10-13 February 2009 in Gippsland, Victoria, Australia.
[31]Tejen Su, Jyunwei Jhang and Chengchih Hou, “A Hybrid Artificial Neural Networks and Particle Swarm Optimization for Function Approximation”, International Journal of Innovative Computing, Information and Control, vol.4, no.9, Sep. 2008.
[32]Kaiqi Zou, Juan Hu and Xiaoyan Kong, “The Structure Optimized Fuzzy Clustering Neural Network Model and Its Application”, International Journal of Innovative Computing, Information and Control, vol.4, no.7, pp.1627-1634, July 2008.
[33]Chu-Chieh Jay Lin and Yu-Chi Sung, “Expert Group Neural Networks for Structural Health Diagnosis of Mau-Lo Creek Cable-Stayed Bridge”, ICIC Express Letters, vol.3, no.1, pp.47-52, 2009.
[34]Y. Wang, “Fuzzy Clustering Analysis by Using Genetic Algorithm”, ICIC Express Letters, vol.2, no.4, pp.331-337, 2008.
[35]H. Tamura, K. Tanno, H. Tanaka and Z. Zhang, “Bi-directional Function Learning Method for Time Series Prediction”, ICIC Express Letters, vol.2, no.4, pp.401-407, 2008.
[36]Fei-Hu Hsieh, Po-Lun Chang, Ying-Kuei Yang, and Ying-Shiu Chen,”Study on Fast-Scale Instability Phenomena of Single-Phase Full-Bridge Inverters”, International Journal of Innovative Computing, Information and Control, vol.5, no.12, Dec. 2009.
[37]Po-Lun Chang, Fei-Hu Hsieh, Hen-Kung Wang, Ying-Kuei Yang, “Chaos Control of Boost Converter”, ICIC Express Letters, vol.3, No.4(A), pp.1107-1112, Dec. 2009.
[38]J.L. Deng, “Control problem of grey systems”, Systems and Control Letters, vol. 5, pp. 288-294, 1982.
[39]D.S. Yi and R. Yang, “Grey predictor controller for DC speed control system”, The Journal of Grey System, vol. 2, pp. 189-215. 1990.
[40]Y.P Huang and T.M. Yu, “Grey models for seasonal calamity forecast and control problems”, The Journal of Grey System, vol. 8, pp.37-56, 1996.
[41]Z.M. Li, “Primary applications of grey system theory in the study of earthquake forecast”, Journal of Seismology, vol. 4, pp. 27-31, 1986.
[42]S.H. Chang, J.H. Wu and L. Zhu, “Frequency synthesizer product or/and process optimization using the grey relational analysis”, The Journal of Grey System, vol. 8, pp.235-60, 1996.
[43]夏郭賢、吳漢雄，”灰關聯分析之線性數據前處理探討”，灰色系統學刊，第一卷，第一期，第47-53頁，1998.
[44]W. M. Lin, C. H. Huang, C. H. Lin, C. M. Chen and L. W. Wang, “Restoration Strategy for Secondary Power Network with Grey Relational analysis”, IET Gener. Transm. Distrib. , 2008, 2, (2), pp. 167-174.
[45]H. Robbins and S. Monro, “A stochastic approximation method”, Ann. Math. Stat., vol.22, no.3, pp.400-407, Sep. 1951.
[46]J. R. Blum, “Approximation methods which converge with probability”, Ann. Math. Stat., vol.25, no.2, pp.382-386, Jun. 1954.
[47]R. Babuska and H.B. Verbruggen, “Constructing Fuzzy Models by Product Space Clustering”, Fuzzy Model Identification. Springer-Verlag, 1997.
[48]Chen-Chia Chuang, Shun-Feng Su, Jin-Tsong Jeng and Chih-Ching Hsiao, “Robust Support Vector Regression Networks for Function Approximation with Outliers”, IEEE trans. On neural networks, 13(6), pp1322~1330, 2002.
[49]D. S. Chen and R. C. Jain, “A robust back-propagation learning algorithm for function approximation”, IEEE Trans. on Neural Networks,5, pp467–479, 1994.
[50]C. C. Chuang, S. F. Su and C. C. Hsiao, “The annealing robust backpropagation (ARBP) learning algorithm”, IEEE Trans. on Neural Networks, 11, pp1067–1077, 2000.
[51]F. E. H. Tay and L. Cao, “Application of support vector machines in financial time series forecasting”, Int. J. Manage., pp309–317, 2001.
[52]J. A. K. Suykens, J. De Brabanter, L. Lukas, and J. Vandewalle, “Weighted least squares support vector machines: Robustness and sparse approximation”, Neurocomputing, 48, pp85-105, 2002.
[53]V. David Sanchez, “Robustization of a learning method for RBF network”, Neurocomputing, 9, pp85~94,1995.
[54]莊鎮嘉, “Robust Approaches of modeling under outlier”, 台科大博士論文,2000.
[55]謝鴻琳, “以模糊群聚為基礎的強健式函數趨近法”, 台科大博士論文,2006.
[56]L.X.Wang and J.M. Mendel,"Generating fuzzy rules by learning from examples", IEEE Trans. on Syst. Man, Cybern. , 22, pp1414-1427, 1992.
[57]T. P. Hong and C.Y. Lee, “Induction of fuzzy rules and membership functions from training examples”, Fuzzy Sets and System, 84, pp33-47, 1996.
[58]K. Nozaki, H. Ishibuchi, and H.Tanaka, ”A simple but powerful heuristic method for generating fuzzy rules from numerical data”, Fuzzy Sets and System, 86, pp251-270, 1997.
[59]R. Thawonmas and S. Abe, “Function approximation based on fuzzy rules extracted from partioned numerical data”, IEEE Trans. on Syst. Man, Cybern. B, 29, pp525-534, 1999.
[60]J. Hollatz, “Fuzzy Identification Using Methods of Intelligent Data Analysis“, Fuzzy Model Identification. Springer-Verlag. 1997.
[61]J. S. Roger Jang, “ANFIS: Adaptive-Network-based Fuzzy Inference Systems”, IEEE Trans. on Syst. Man, Cybern. 23(03), pp 665-685, 1993.
[62]R. J. S. Jang, C. T. Sun and E. Mizutani, Neuro-fuzzy and Soft Computing, Prentice Hall, 1997.
[63]Shiqian Wu, Meng Joo Er, and Yang Gao, “ A Fast Approach for Automatic Generation of Fuzzy Rules by Generalized Dynamic Fuzzy Neural Network", IEEE Trans. on Fuzzy Systems, 9 (4), pp578-594,2001.
[64]Y.H. Lin and G. A. Cunningham, “A new approach to fuzzy-neural system modeling", IEEE Trans. on Fuzzy Systems, 3, pp190-197,1995.
[65]C. R. Wylie and A. Barrett, Advanced Engineering Mathematics, pp840~pp846, McGraw-Hill, New York, 1982.
[66]Frank Hoppner, Frank Klwawonn, Rudolf Kruse and Thomas Runkler, Fuzzy Cluster Analysis, John Wiley & Sons, Inc., New York, 1999.
[67]Yager R. and Filev D. P. Essentials of Fuzzy Modeling and Control. Wiley, New York, 1994.
[68]Horng-Lin Shieh, Ying-Kuei Yang and Chien-Nan Lee, “A Robust Approach of Fuzzy Clustering on Data Sets with Noise and Outliers”, Cybernetics and Systems: An International Journal, Vol.37, No.7, pp. 755-778, 2006.
[69]顏月珠，現代統計學, 三民書局，民國82年2月.
[70]Chen-Chia Chuang, Jin-Tsong Jengb, Pao-Tsun Lin, “Annealing robust radial basis function networks”, Neurocomputing, 56, pp123-139, 2004.
[71]M. Sugeno and T. A Yasukawa, “Fuzzy-Logic-Based Approch to Qualitative Modeling”, IEEE Trans. on Fuzzy Systems, vol 1. , pp.7-31, 1993.
[72]T. Takagi and M. Sugeno, “Fuzzy Identification of System and Its Applications to Modeling and Control”, IEEE Trans. on System, Man and Cybernetics, vol SMC-15, no 1 pp.116-132, 1985.
[73]J. H. B. Deane and D. C. Hamill, “Instability, subharmonics and chaos in power electronics systems”, IEEE Trans. Power Electron., vol. 5, no. 3, pp. 260-268, 1990.
[74]J. H. B. Deane and D. C. Hamill, “Analysis, simulation, and experimental study of chaos in the buck converter”, IEEE Power Electron. Specialists Conf., 1990, pp. 491-498.
[75]J. H. B. Deane, “Chaos in a current-mode controlled boost DC-DC converter”, IEEE Trans. Circuits and Syst. I, vol. 39, no. 8, pp. 680-683, 1992.
[76]E. Ott, C. Grebogi and J. A. Yorke, “Controlling Chaos”, Phys. Rev. Lett., pp. 1196-1199, 1990.
[77]K. Pyragas, “Control of chaos by self-controlling feedback”, Phys. Lett., pp. 421-428, 1992.
[78]Y. Zhou, H. H. C. Iu, C. K. Tse, and J. N. Chen, “Controlling chaos in DC/DC converters using optimal resonant parametric perturbation”, IEEE ISCAS'05, vol. 3, 2005, pp. 2481-2484.
[79]A. Kavitha, G. Uma, “Control of chaos by resonant parametric perturbation in a current mode controlled buck-boost Dc-Dc converter”, IEEE APEC 2008, pp. 323-327, 24-28 Feb. 2008.
[80]Junyan Yi, Gang Yang, Yunyi Zhu and Zheng Tang, “Dynamics Analysis and a coefficient Tuning Method in a Chaotic Neural Network”, ICIC Express Letters, vol.2, no.4, pp.323-330, Dec. 2009.