本論文首先以終端滑模控制方法，提出用於機器手臂之新型多輸入輸出適應性模糊終端滑模控制器設計方式。此控制器結合了模糊邏輯控制器、終端滑模控制器、及適應性架構，除了保留終端滑模控制的優勢也減緩終端滑模控制的顫動現象，其可調參數也提升了模糊終端滑模控制器的性能，所以此控制器不須精確的系統參數。終端滑模控制器具有可於有限時間內將系統追蹤誤差收斂為零的特性，但顫動現象仍然是終端滑模控制存在的問題。本論文也針對非線性多變數系統提出終端滑動函數控制器，先設計一個適當的終端滑動函數，並將此函數加入控制器，基於李亞諾夫穩定理論，終端滑動函數控制器可保證此非線性多變數系統是均勻最終有界。不同於終端滑模控制使用不連續的切換控制，終端滑動函數控制使用連續的滑動函數控制，因此避免顫動問題。
緊接著，針對二個參數不匹配混沌系統之信號同步問題，設計一個適應性高木-菅野模糊終端滑動函數控制器。此控制器結合了適應性架構及高木-菅野模糊終端滑動函數控制器，可保證混沌系統之同步誤差為均勻最終有界。最後，提出一個以高木-菅野模糊模型之參數估測為基礎的適應性終端滑動函數控制器。先以高木-菅野模糊模型表示受控體，此高木-菅野模糊模型的參數可線上調整以估測非線性受控體參數，然後以終端滑動函數控制此受控體，此整合的架構同時具有強健及快速收斂的優勢。模擬結果顯現這些控制器具有良好的性能。

A new design approach of a multiple-input-multiple-output (MIMO) adaptive fuzzy terminal sliding-mode controller (AFTSMC) for robotic manipulators is developed in this dissertation. The AFTSMC, incorporating the fuzzy logic controller (FLC), the terminal sliding-mode controller (TSMC), and an adaptive scheme, is designed to retain the advantages of the TSMC while reducing the chattering. The self-tuning parameters are adapted online to improve the performance of the fuzzy terminal sliding-mode controller (FTSMC). Thus, it does not require detailed system parameters for the presented AFTSMC. The terminal sliding-mode controller can drive system tracking errors to converge to zero in finite time. Unfortunately, chattering still remains a problem in terminal sliding-mode control. This dissertation also presents a terminal sliding-function controller (TSFC) approach for controlling a class of nonlinear multivariable systems with uncertainties. An appropriate TSF is designed and then applied to the control law. Based on the Lyapunov stability theory, the TSFC for the nonlinear multivariable system guarantees that the system states are uniformly ultimately bounded (UUB). Different from classical terminal sliding-mode control, which uses a discontinuous switching control law, the TSF control uses a continuous control law and thus avoids the chattering problem.
Next, an adaptive Takgi-Sugeno (T-S) fuzzy terminal sliding function-controller (AFTSFC) approach to synchronize two chaotic systems with parameter mismatch is presented in this dissertation. We incorporated the adaptive algorithm and T-S fuzzy terminal sliding-function control approaches. The proposed AFTSFC guarantees that the synchronization errors are UUB. Finally, an adaptive terminal sliding-function controller (ATSFC) based on parameter estimation of the T-S fuzzy model approach is presented in this dissertation. The plant is represented using the T-S fuzzy model. Based on the Lyapunov stability criteria, the parameters of the T-S fuzzy model are adapted online to estimate a nonlinear uncertain plant system. The ATSFC scheme can achieve a robust and fast convergent performance. The simulation results demonstrate that these methods can provide a reasonable performance.

[1] S. Boyd, L. E. Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia, PA: SIAM, 1994.
[2] R. K. Barai and K. Nonami, “Optimal two-degree-of-freedom fuzzy control for locomotion control of a hydraulically actuated hexapod robot,” Information Sciences, vol. 177, pp. 1892–1915, 2007.
[3] Y. Chang, “Adaptive sliding mode control of multi-input nonlinear systems with perturbations to achieve asymptotical stability,” IEEE Transactions on Automatic Control, vol. 54, no. 12, pp. 2863–2869, Dec. 2009.
[4] E. Cherrier, M. Boutayeb, and J. Ragot, “Observers-based synchronization and input recovery for a class of nonlinear chaotic models,” IEEE Transactions on Circuits Systems I, Regular Papers, vol. 53, no. 9, pp. 1977-1988, Sep. 2006.
[5] S. Celikovsky and G. Chen, “Secure synchronization of a class of chaotic systems from a nonlinear observer approach,” IEEE Transactions on Automatic Control, vol. 50, no. 1, pp. 76-82, Jan. 2005.
[6] C.-Y. Chen, T.-H. S. Li, and Y.-C. Yeh, “EP-based kinematic control and adaptive fuzzy sliding-mode dynamic control for wheeled mobile robots,” Information Sciences, vol. 179, pp. 180–195, 2009.
[7] Y. W. Cho and C. W. Park, “An indirect model reference adaptive fuzzy control for SISO Takagi-Sugeno model,” Fuzzy Sets and Systems, vol. 131, pp. 197-215, 2002.
[8] P. B. Deshpande and R. H. Ash, Computer Process Control with Advanced Control Applications, second ed., Instrument Society of America, North Carolina, 1988.
[9] F. Da and W. Song, “Fuzzy neural networks for direct adaptive control,” IEEE Transactions on Industrial Electronics, vol.11, pp. 1471-1480, 2003.
[10] J. Dong, Y. Wang, and G.-H. Yang, “Control synthesis of continuous-time T-S fuzzy Systems with local nonlinear models,” IEEE Transactions on Systems, Man, and Cybernetics- Part B: Cybernetics, vol. 39, no. 5, pp. 1245-1258, Oct. 2009.
[11] Y. Feng, X. Yu, and Z. Man, “Non-singular terminal sliding mode control of rigid manipulators,” Automatica, vol. 38, pp. 2159–2167, 2002.
[12] Y. Guo and P.-Y. Woo, “An adaptive fuzzy sliding mode controller for robotic manipulators,” IEEE Transactions on Systems, Man, and Cybernetics- Part A: Systems and Humans, vol. 33, pp. 149-159, 2003.
[13] P. J. Guo, X. Z. Wei, K. S. Tang, and G. Chen, “Integral-observer-based chaos synchronization,” IEEE Transactions on Circuits Systems II, Express Briefs, vol. 53, no. 2, pp. 110-114, Feb. 2006.
[14] Y.-C. Hsu, G. Chen, and H.-X. Li, “A fuzzy adaptive variable structure controller with applications to robotic manipulators,” IEEE Transactions on Systems, Man, and Cybernetics- Part B: Cybernetics, vol. 31, pp. 331-340, 2001.
[15] J. Y. Hung, W. Gao, and J. C. Huang, “Variable structure control: a survey,” IEEE Transactions Industrial Electronics, vol. 40, pp. 2-22, 1993.
[16] Y.-J Huang, T.-C. Kuo, and S.-H. Chang, “Adaptive sliding-mode control for nonlinear systems with uncertain parameters,” IEEE Transactions on Systems, Man, and Cybernetics- Part B: Cybernetics, vol.38, pp. 534-539, 2008.
[17] M.-Y. Hsiao, T.-H. S. Li, J.-Z. Lee, C.-H. Chao, and S.-H. Tsai, “Design of interval type-2 fuzzy sliding-mode controller,” Information Sciences, vol. 178, pp. 1696-1716, 2008.
[18] D. Huang and S. K. Nguang, “Static output feedback controller design for fuzzy systems: An ILMI approach,” Information Sciences, vol. 177, pp. 3005-3015, 2007.
[19] H. F. Ho, Y. K. Wong, and A. B. Rad, “Robust fuzzy tracking control for robotic manipulators,” Simulation Modelling Practice and Theory, vol. 15 pp. 801–816, 2007.
[20] S. Janardhanan and B. Bandyopadhyay, “On discretization of continuous-time terminal sliding mode,” IEEE Transactions on Automatic Control, vol. 51, pp. 1532-1536, 2006.
[21] H. K. Khalil, Nonlinear Systems, Prentice Hall, N.J., 2002.
[22] J. H. Kim, C. H. Hyun, E. Kim, and M. Park, “Adaptive synchronization of uncertain chaotic systems based on T-S fuzzy model,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 359-369, June 2007.
[23] C.-L. Kuo, T.-H. S. Li, and N. R. Guo, “Design of a novel fuzzy sliding-mode control for magnetic ball levitation system,” Journal of Intelligent and Robotic Systems, vol. 42, pp. 295-316, 2005.
[24] C.-K. Lin, “Nonsingular terminal sliding mode control of robot manipulators using fuzzy wavelet networks,” IEEE Transactions on Fuzzy Systems, vol. 14, pp. 849-859, 2006.
[25] C.-K. Lin, “Robust adaptive critic control of nonlinear systems using fuzzy basis function networks: An LMI approach,” Information Sciences, vol. 177, pp. 4934–4946, 2007.
[26] A. Levant and L. Alelishvili, “Integral high-order sliding modes,” IEEE Transactions on Automatic Control, vol. 52, no. 7, pp. 1278–1282, July 2007.
[27] J. Lu, J. Cao, and D. W. C. Ho, “Adaptive stabilization and synchronization for chaotic Lur’e systems with time-varying delay,” IEEE Transactions on Circuits Systems I, Regular Papers, vol. 55, no. 5, pp. 1347 - 1356, 2008.
[28] K. Y. Lian, T. S. Chiang, C. S. Chiu, and P. Liu, “Synthesis of fuzzy model-based designs to synchronization and secure communications for chaotic systems,” IEEE Transactions on Systems, Man, and Cybernetics- Part B: Cybernetics, vol. 31, no.1, pp. 66 – 83, Feb. 2001.
[29] K. Y. Lian, C. S. Chiu, T. S. Chiang, and P. Liu, “LMI-based fuzzy chaotic synchronization and Communications,” IEEE Transactions on Fuzzy Systems, vol. 9, no. 4, pp. 539-553, Aug. 2001.
[30] T.-H. S. Li, M.-Y. Hsiao, J.-Z. Lee, and S.-H. Tsai, “Controlling a time- varying unified chaotic system via interval type 2 fuzzy sliding-mode technique,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, pp. 171-180, 2009.
[31] J.-C. Lo and Y.-H. Kuo, “Decoupled fuzzy sliding-mode control,” IEEE Transactions on Fuzzy Systems, vol. 6, no. 3, pp. 426-435, Aug. 1998.
[32] T. H. S. Li, C. L. Kuo, and N. R. Guo, “Design of an EP-based fuzzy sliding-mode control for a magnetic ball suspension system,” Chaos Solitons Fractals, vol.33, pp. 1523-1531, Aug. 2007.
[33] T.-H. S. Li and K.-J. Lin, “Stabilization of singularly perturbed fuzzy systems,” IEEE Transactions on Fuzzy Systems, vol. 12, pp. 579-595, 2004.
[34] T.-H. S. Li, J.-Z. Lee, M.-Y. Hsiao, and S.-H. Tsai, “Robust interval fuzzy control of a class of uncertain chaotic system,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, pp. 181-190, 2009.
[35] H. K. Lam, W. K. Ling, H. C. Iu, and S. H. Ling, “Synchronization of chaotic systems using time-delayed fuzzy state-feedback controller,” IEEE Transactions on Circuits Systems I, Regular Papers, vol. 55, no. 3, pp. 893-903, Apr. 2008.
[36] J.-H. Li, T.-H. S. Li, and T.-H. Ou, “Design and implementation of fuzzy sliding mode controller for a wedge balancing system,” Journal of Intelligent and Robotic Systems, vol. 37, pp. 285-306, 2003.
[37] K.-Y Lian, C.-H. Su, and C.-S. Huang, “Performance enhancement for T–S fuzzy control using neural networks,” IEEE Transactions on Fuzzy Systems, vol. 14, pp. 619-627, 2006.
[38] H. K. Lam and L. D. Seneviratne, “Chaotic synchronization using sampled-data fuzzy controller based on fuzzy-model-based approach,” IEEE Transactions on Circuits Systems I, Regular Papers, vol. 55, no. 3, pp. 883 – 892, Apr. 2008.
[39] T. H. S. Li, and S.-H. Tsai, “T-S fuzzy bilinear model and fuzzy controller design for a class of nonlinear systems,” IEEE Transactions on Fuzzy Systems, vol. 15, no. 3, pp. 494-506, June 2007.
[40] K. Y. Lian and H. W. Tu, “LMI-based adaptive tracking control for parametric strict-feedback systems,” IEEE Transactions on Fuzzy Systems, vol. 16, pp. 381-392, 2008.
[41] T.-H. S. Li, S.-H. Tsai, and M.-Y. Hsiao, “Robust fuzzy control for a class of time-delay fuzzy bilinear systems with an additive disturbance,” International Journal of Nonlinear Sciences and Numerical Simulation, vol. 10, pp. 315-322, 2009.
[42] Y.-J. Liu and W. Wang, “Adaptive fuzzy control for a class of uncertain nonaffine nonlinear systems,” Information Sciences, vol. 177, pp. 3901-3917, 2007.
[43] Y.-W. Liang, S.-D. Xu, D.-C. Liaw, and C.-C. Chen, “A study of T-S model-based SMC scheme with application to robot control,” IEEE Transactions on Industrial Electronics, vol. 55, pp. 3964-3971, 2008.
[44] J. B. Mbede, P. Ele, C.-M. Mveh-Abia, Y. Toure, V. Graefe, and S. Ma, “Intelligent mobile manipulator navigation using adaptive neuro-fuzzy systems,” Information Sciences, vol. 171, pp. 447-474, 2005.
[45] B. Mansouri, N. Manamanni, K. Guelton, A. Kruszewski, and T.M. Guerra, “Output feedback LMI tracking control conditions with H∞ criterion for uncertain and disturbed T–S models,” Information Sciences, vol. 179, pp. 446–457, 2009.
[46] T. R. Oliveira, A. J. Peixoto, and L. Hsu, “Sliding mode control of uncertain multivariable nonlinear systems with unknown control direction via switching and monitoring function,” IEEE Transactions on Automatic Control, vol. 55, no. 4, pp. 1028–1034, Apr. 2010.
[47] W. Pedrycz, “Why triangular membership functions,” Fuzzy Sets and Systems, vol. 64, pp. 21–30, 1994.
[48] W. Pedrycz, “Fuzzy equalization in the construction of fuzzy sets,” Fuzzy Sets and Systems, vol. 119, pp. 329–335, 2001.
[49] 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: Cybernetics, vol. 34, pp. 2293-2302, 2004.
[50] W. Pedrycz and F. Gomide, An Introduction to Fuzzy Sets: Analysis and Design, MIT Press, Cambridge, MA, 1998.
[51] C. W. Park and M. Park, “Adaptive parameter estimator based on T-S fuzzy models and its applications to indirect adaptive fuzzy control design,” Information Sciences, vol. 159, pp. 125-139, 2004.
[52] R.-E. Precup and S. Preitl, “PI-Fuzzy controllers for integral plants to ensure robust stability,” Information Sciences, vol. 177, pp. 4410–4429, 2007.
[53] W. Pedrycz, and J. Valente de Oliveira, “A development of fuzzy encoding and decoding through fuzzy clustering,” IEEE Transactions on Instrumentation and Measurement, vol. 57, pp. 829-837, 2008.
[54] M. Roopaei and M. Z. Jahromi, “Chattering-free fuzzy sliding mode control in MIMO uncertain systems,” Nonlinear Analysis, vol. 71, pp. 4430-4437, 2009.
[55] M. Sun, S. S. Ge, and I. M. Y. Mareels, “Adaptive repetitive learning control of robotic manipulators without the requirement for initial repositioning,” IEEE Transactions on Robotics, vol. 22, pp. 563-568, 2006.
[56] J. J. E. Slotine and W. Li, Applied Nonlinear Control, Prentice-Hall, Englewood Cliffs, NJ, 1991.
[57] C.-S. Ting, “An observer-based approach to controlling time-delay chaotic systems via Takagi–Sugeno fuzzy model,” Information Sciences, vol. 177, pp. 4314–4328, 2007.
[58] C. W. Tao, M.-L. Chan, and T.-T. Lee, “Adaptive fuzzy sliding mode controller for linear systems with mismatched time-varying uncertainties,” IEEE Transactions on Systems, Man, and Cybernetics- Part B: Cybernetics, vol. 33, no. 2, pp. 283-294, April 2003.
[59] K. Tanaka, T. Ikeda, and H. O. Wang, “A unified approach to controlling chaos via an LMI-based fuzzy control system design,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 45, no. 10, pp. 1021-1040, Oct. 1998.
[60] S. Tong, Y. Li, and P. Shi, “Fuzzy adaptive backstepping robust control for SISO nonlinear system with dynamic uncertainties,” Information Sciences, vol. 179, pp. 1319–1332, 2009.
[61] C.W. Tao, J. S. Taur, and M.-L. Chan, “Adaptive fuzzy terminal sliding mode controller for linear systems with mismatched time-varying uncertainties,” IEEE Transactions on Systems, Man, and Cybernetics- Part B: Cybernetics, vol. 34, pp. 255-262, 2004.
[62] L. Wang, T. Chai, and L. Zhai, “Neural-network-based terminal sliding mode control of robotic manipulators including actuator dynamics,” IEEE Transactions on Industrial Electronics, vol. 56, pp. 3296-3304, 2009.
[63] J. Wang , D. Q. Guo , and B. Deng, “Observer-based robust adaptive variable universe fuzzy control for chaotic system,” Chaos Solitons Fractals, vol. 23, no. 3, pp. 1013-1032, Feb. 2005.
[64] Y. W. Wang, Z. H. Guan, and H. O. Wang, “LMI-based fuzzy stability and synchronization of Chen’s system,” Physics Letters A, vol. 320, no. 2-3, pp. 154–159, Dec. 2003.
[65] L. K. Wong, F. H. F. Leung, and P. K. S. Tam, “A fuzzy sliding controller for nonlinear systems,” IEEE Transactions on Industrial Electronics, vol. 48, pp. 32-37, 2001.
[66] H. T. Yau, “Design of adaptive sliding mode controller for chaos synchronization with uncertainties,” Chaos Solitons Fractals, vol. 22, no. 2, pp. 341–347, Oct. 2004.
[67] J. Yoneyama, “Robust stability and stabilizing controller design of fuzzy systems with discrete and distributed delays,” Information Sciences, vol. 178, pp. 1935–1947, 2008.
[68] N. Yagiz, Y. Hacioglu, and Y. Taskin, “Fuzzy sliding-mode control of active suspensions,” IEEE Transactions on Industrial Electronics, vol. 55, pp. 3883-3890, 2008.
[69] Y. C. Yeh, T. H. S. Li, and C. Y. Chen, “Adaptive fuzzy sliding-mode control of dynamic model based car-like mobile robot,” International Journal of Fuzzy Systems, vol. 11, pp. 272-286, 2009.
[70] S.-J. Yoo, J.-B. Park, and Y.-H. Choi, “Adaptive dynamic surface control of flexible-joint robots using self-recurrent wavelet neural networks,” IEEE Transactions on Systems, Man, and Cybernetics- Part B: Cybernetics, vol. 36, pp. 1342-1355, 2006.
[71] J. J. Yan, Y. S. Yang, T. Y. Chiang, and C.Y. Chen, “Robust synchronization of unified chaotic systems via sliding mode control,” Chaos Solitons Fractals, vol. 34, no. 3, pp. 947-954 Nov. 2007.
[72] X. H. Yu, and M. Zhihong, “Fast terminal sliding-mode control design for nonlinear dynamical systems,” IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, vol. 49, pp. 261-264, 2002.
[73] L. A. Zadeh, “Is there a need for fuzzy logic,” Information Sciences, vol. 178, pp. 2751–2779, 2008.
[74] M. Zhihong, A. P. Paplinski, and H. R. Wu, “A robust MIMO terminal sliding mode control scheme for rigid robotic manipulators,” IEEE Transactions on Automatic Control, vol. 39, pp. 2464-2469, 1994.
[75] H. Zhang, Y. Xie, Z. Wang, and C. Zheng, “Adaptive synchronization between two different chaotic neural networks with time delay,” IEEE Transactions on Neural Networks, vol. 18, no. 6, pp. 1841-1845, 2007.
[76] M. Zhihong and X. H. Yu, “Terminal sliding mode control of MIMO linear systems,” IEEE Transactions on Circuits and Systems I, vol. 44, pp. 1065-1070, 1997.