在本論文中，提出一個簡化的蟻群最佳演算法與其在模糊類神經網路之應用。傳統上螞蟻群聚最佳演算法屬於在解離散組合最佳化問題，其需要複雜的演算流程。因此，在本篇論文中提出一個連續最佳化的方法。並將此方法與模糊類神經網路做結合，應用於函數近似、非線性系統的模組化、以及非線性系統的控制。針對函數近似與非線性系統的模組化的應用，模糊類神經網路的權重值因子能透過離線學習的程序來做調整。於非線性系統控制應用上，分別考慮多輸入多輸出、狀態與輸出回授之非線性系統，藉由即時調整模糊類神經網路的參數以完成控制目的。在多輸入多輸出非線性系統控制設計中，其控制觀點結合了倒階的設計技術與模糊類神經網路。根據其控制的技術，其模糊類神經倒階控制器經由蟻群最佳演算法的方法來做參數的即時調整。針對狀態或輸出回授控制設計，藉著使用直接型控制器的設計概念，與在本篇論文中所提出的簡化的蟻群最佳演算法為基礎的B-spline模糊類神經控制器來控制非線性系統。為了要線上調整這些參數與評估閉迴路系統穩定性的目的，我們提出一個能量適應函數於簡化的蟻群最佳演算法中。並藉著Lyapunov函數來做閉迴路系統的穩定度分析。另外，為了保證閉迴路系統的穩定度，監督式控制器會被利用來與簡化的蟻群最佳演算法為基礎的B-spline模糊類神經控制做結合。最後從模擬結果驗證其所提出方法的可行性與適用性。

In this thesis, a compact ant colony optimization algorithm (CACOA) of fuzzy-neural networks is proposed. Traditionally, ant colony optimization algorithms solve discrete combinatorial optimization problems, and always need complicated operation procedures. Therefore, a continuous ant colony optimization algorithm is proposed for function approximation, nonlinear system modeling, and nonlinear system control. For function approximation and nonlinear system modeling, the weighting factors of the fuzzy-neural networks can be tuned through off-line learning procedure. For a class of multiple-input multiple-output (MIMO) nonlinear systems, the control scheme incorporates backstepping technique with the fuzzy neural networks, and the adjusted parameters of the fuzzy neural networks are tuned on-line via the CACOA approach. For state-feedback and output-feedback control, based on the direct adaptive control approach, a B-spline fuzzy-neural controller using CACOA is proposed to control a class of nonlinear systems. For the purpose of on-line tuning these parameters and evaluating the stability of the closed-loop system, an energy fitness function is included in the CACOA approach. The stability of the closed-loop system is analyzed by means of Lyapunov functions. In addition, in order to guarantee the stability of the closed-loop nonlinear system, a supervisory controller is incorporated into the CACOA-based B-spline fuzzy neural controller. Finally, the simulation results demonstrate the feasibility and applicability of the proposed method.

[1] K. Hornik, M. Stinchcombe, and H. White, “Multilayer feedforward networks are universal approximators,” Neural Networks, no. 2, pp. 359-366, 1989.
[2] L. X. Wang, Adaptive Fuzzy Systems and Control, Prentice Hall, 1994.
[3] 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.
[4] 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.
[5] C. T. Lin, and L. Siana, “An Efficient Human Detection System Using Adaptive Neural Fuzzy Networks,” International Journal of Fuzzy Systems, vol. 10, no. 3, pp. 150-160, 2008.
[6] S. Wu, M. J. Er, and Y. Gao, “A fast approach for automatic generation of fuzzy rules by generalized dynamic fuzzy neural networks,” IEEE Transactions on HFuzzy SystemsH, vol. 9, pp.578-594, 2001.
[7] 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.
[8] Y. G. Leu, T. T. Lee, and W. Y. Wang, “On-line tuning of fuzzy neural network for adaptive control of nonlinear dynamic systems,” IEEE Transactions on HSystemsH, Man, and Cybernetics, Part B, vol. 27, pp. 1034–1043, Dec. 1997.
[9] T. Y. Kim and J. H. Han, “Edge representation with fuzzy sets in blurred images,” Fuzzy Sets HSystemsH, vol. 100, pp. 77–87, 1998.
[10] Z. Yang, T. Hachino, and T. Tsuji, “Model reduction with time delay combining the least-squares method with the genetic algorithm,” IEE Proc. Control Theorem Appl., vol. 143, no. 3, 1996.
[11] M. Dorigo, M. Birattari, and T. Stiitzle, “Ant Colony Optimization,” IEEE Computational Intelligence Magazine, Nov. 2006.
[12] C. T. Man, X. X. Li, and L. Y. Zhang, “Radial Basis Function Neural Network Based on Ant Colony Optimization,” IEEE International Conference on Computational Intelligence and Security Workshops, pp. 59-62, Dec. 2007.
[13] R. S. Parpinelli, H. S. Lopes, and A. A. Freitas, “Data mining with an ant colony optimization algorithm,” IEEE Transactions Evolutionary Computing, vol. 6, no. 4, pp. 321-332, Aug. 2002.
[14] K. M. Sim and W. H. Sun., “Ant colony optimization for routing and load-balancing: survey and new directions,” IEEE Transactions on HUSystemsUH, Man, and Cybernetics, Part A: System and Humans, vol. 33, no. 5, pp. 560-572, Sep. 2003.
[15] J. Cassillas, O. Cordon, and F. Herrera, “Learning fuzzy rules using ant colony optimization algorithms,” Proc. Workshop on Ant Algorithms from Ant Colonies to Artificial Ants, pp. 13-21, Brussels, Belgium, Sep. 2000.
[16] A. Isidori, Nonlinear Control System. New York: Springer-Verlag, 1989.
[17] M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
[18] I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “Systematic design of adaptive controller for feedback linearizable system,” IEEE Transactions Automat. Contr., vol. 36, pp. 1241–1253, 1991.
[19] C. Kwan and F. L. Lewis, “Robust backstepping control of nonlinear systems using neural networks,” IEEE Transactions on HSystemsH, Man, and Cybernetics, Part A, vol. 30, pp. 753–765, 2000.
[20] T. Knohl and H. Unbehauen, “ANNNAC—extension of adaptive backstepping algorithm with artificial neural networks,” Inst. Elect. Eng. Proc. Contr. Theory Appl., vol. 147, pp. 177–183, 2000.
[21] C. M. Kwan and F. L. Lewis, “Robust backstepping control of induction motors using neural networks,” IEEE Transactions Neural Networks, vol. 11, pp. 1178–1187, 2000.
[22] J. Y. Choi and J. A. Farrell, “Adaptive observer backstepping control using neural networks,” IEEE Transactions Neural Networks, vol. 12, pp. 1103–1112, 2001.
[23] Y. Zhang, P.Y. Peng, and Z.P. Jiang, “Stable Neural Controller Design for Unknown Nonlinear Systems Using Backstepping,” IEEE Transactions on Neural Networks, vol. 11, no. 6, Nov. 2000.
[24] 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, Sep. 2006.
[25] S. S. Sastry and A. Isidori, “Adaptive control of linearization systems,” IEEE Transactions Automat. Contr., vol. 34, pp. 1123–1131, 1989.
[26] R. Marino and P. Tomei, “Globally adaptive output-feedback control of nonlinear systems, part I: Linear parameterization,” IEEE Transactions Automat. Contr., vol. 38, pp. 17–32, Jan. 1993.
[27] R. Marino and P. Tomei, “Globally adaptive output-feedback control of nonlinear systems, part II: Nonlinear parameterization,” IEEE Transactions Automat. Contr., vol. 38, pp. 33–48, Jan. 1993.
[28] I. Kanellakopoulos, P. V. Kokotovic, and A. S. Morse, “Systematic design of adaptive controllers for feedback linearizable systems,” IEEE Transactions Automat. Contr., vol. 36, pp. 1241–1253, Nov. 1991.
[29] W. Y. Wang, M. L. Chan, T. T. Lee, and C. H. Liu, “Recursive Back-stepping Design of Adaptive Fuzzy Controller for Strict Output Feedback Nonlinear Systems,” Asian Journal of Control, vol. 4, no.3, Sep. 2002.
[30] L. X. Wang, “A Supervisory Controller for Fuzzy Control Systems that Guarantees Stability,” IEEE Transactions On Automatic Control, vol. 39, no. 9, pp.1845-1847, 1994.
[31] Y.G. Leu, T.T. Lee, and W.Y. Wang, “Observer-based Adaptive Fuzzy-Neural Control for Unknown Nonlinear Dynamical Systems,” IEEE Transactions on HSystemsH, Man, and Cybernetics. Part B: Cybernetics, vol. 29, no. 5, pp.583-591, Oct., 1999.
[32] C.H. Wang, H.L. Liu, T.C. Lin, “Direct adaptive fuzzy-neural control with state observer and supervisory controller for unknown nonlinear dynamical systems,” IEEE Transactions on HFuzzy SystemsH, vol. 10, no.1, pp.39-49, 2002.
[33] W. Y. Wang, C. Y. Cheng, and Y. G. Leu, “An online GA-based output-feedback direct adaptive fuzzy-neural controller for nonlinear systems,” IEEE Transactions on HSystemsH, Man, and Cybernetics, Part B, vol. 34, pp.334-345, Feb. 2004.
[34] W. Y. Wang, and Yi-Hsum Li, “Evolutionary Learning of BMF Fuzzy-Neural Networks Using a Reduced-Form Genetic Algorithm,” IEEE Transactions on HSystemsH, Man, and Cybernetics. Part B: Cybernetics, vol. 33, no. 6, Dec. 2003.
[35] M. Dorigo, V. Maniezzo, and A. Colorni, “The Ant System: An Autocatalytic Optimizing Process,” Technical Report No. 91-016 Revised, Politecnicodi Milano, Italy, 1991.
[36] M. Dorigo and L.M. Gambardella, “Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem,” IEEE Transactions Evolutionary Computing, vol. 1, no. 1, pp. 53-66, April. 1997.
[37] M. Dorigo, V. Maniezzo, and A. Colorni, “Ant System: Optimization by a colony of cooperating agents,” IEEE Transactions on HSystemsH, Man, and Cybernetics. Part B: Cybernetics, vol. 26, no. 1, Feb. 1996.
[38] B. Bullnheimer, R.F. Hartl, and C. Strauss, Meta-Heuristic: Advances and Trends in Local Search Paradigms for Optimization. Kluwer, Boston, pp 285-296, 1999.
[39] V. Maniezzo, and A. Carbonaro, “An ANTS Heuristic for the Frequency Assignment Problem,” Future Generation Computer Systems, Vol. 16, pp. 927-935, June 2000.
[40] E.G. Talbi, O. Roux, C. Fonlupt, and D. Robillard, “Parallel Ant Colonies for the quadratic assignment problem,” Future Generation Computer Systems, Vol. 17, pp. 441-449, Janu. 2001.
[41] P.S. Shelokar, V.K. Jayaraman, and B.D. Kulkarni, “An Ant Colony Approach for Clustering,” Analytica Chimica Acta, vol. 509, pp. 187-195, May 2004.
[42] S. S. Sastry and M. Bodson, Adaptive Control: Stability, Convergence, and Robustness. Englewood Cliffs, NJ: Prentice-Hall, 1989.
[43] H.B. Zhang, C.U. Li, and X.F. Liao, “Stability Analysis and H∞ Controller Design of Fuzzy Large-Scale Systems Based on Piecewise Lyapunov Functions,” IEEE Transactions on Systems, Man, and Cybernetics, part B, vol. 36, no. 3, June 2006.
[44] K. S. Tsakalis and P. A. Ioannou, Linear Time-Varying Systems. Englewood Cliffs, NJ: Prentice-Hall, 1993.
[45] P. A. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
[46] H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
[47] S. I. Grossman, and W. R. Derrick, Advanced Engineering Mathematics, Happer & Row, 1998.