本研究針對具有不確定項及外部干擾的非線性系統，設計H∞適應性模糊複合控制器來控制，使其輸出響應符合設計者的要求。本文使用模糊邏輯系統來估測非線性不確定項，但由於模糊邏輯系統中的估測參數選擇並沒有限制，因此，本文引入適應性控制來隨著時間調整其參數，以達到最佳估測的目的。為了處理外部干擾與前述估測項所產生的估測誤差，本論文使用H∞控制器，將估測誤差與外部干擾對系統受控輸出的影響降低至預設之一定值以下，以求得能滿足預設性能之H∞適應性模糊複合控制器。
在控制器設計中，吾人使用雙曲正切(hyperbolic tangent , tanh(.))函數取代常用的符號函數(sign(.))，旨在避免震顫現象(chattering phenomenon)且在不影響H∞最終效能的情況下，加快誤差收斂速度。
最後，本研究以倒單擺系統和機械手臂系統為例子，執行電腦模擬，來驗證本研究所設計的H∞適應性模糊複合控制器的可行性。模擬結果顯示其具有良好的追蹤性能與強健性。

In this paper, the H∞-adaptive-fuzzy controller is proposed to control nonlinear systems with external disturbances and uncertainties in order to match the desired performance specified by the designers.
In the proposed controller, a fuzzy logic system (FLS) is used in this study to approximate the nonlinear uncertain terms of the systems. However, since the selection of adjustable parameters is varying and unlimited, the adaptive control law is applied to adjust these parameters systematically. To handle the ill-effects of disturbances and estimated errors on the controlled outputs, the H∞ control methodology is then utilized to suppress the supremum norms between the exogenous inputs w(t) and the controlled outputs e(t).
Besides, a hyperbolic tangent function (tanh(.)), instead of the sign function (sign(.)), is used in the proposed controller to avoid the chattering phenomenon and to achieve the desired H∞ tracking performance as well as to attenuate the convergent errors.
Finally, an inverted pendulum and a robot manipulator are used as examples to demonstrate the feasibility of the proposed H∞-adaptive-fuzzy controller. The simulation results attest good tracking performance and nice robustness in both examples.

[1] B.S. Chen, C.H. Lee, Y.C. Chang, " Tracking Design of
Uncertain Nonlinear SISO Systems: Adaptive Fuzzy Approach",
IEEE Trans. on Fuzzy Systems, Vol.4, No.1, pp.32-43, 1996.

[2] C.C. Kung, T.H. Chen, " tracking-based adaptive fuzzy
sliding mode controller design for nonlinear systems", IET Control
Theory Appl., Vol.1, No.1, pp.82-89, January 2007.

[3] C.C. Kung, T.H. Chen, L.H. Kung, "Modified Adaptive Fuzzy
Sliding Mode Controller for Uncertain Nonlinear Systems", IEICE
Trans. Fundamentals, Vol. E88-A, No.5, pp.1328-1334, May 2005.

[4] C.N. Hwang, "Tracking controllers for robot manipulators",
Master Dissertation, Michigan State University, 1986.

[5] H.F. HO, Y.K. Wong, A.B. Rad, "Adaptive fuzzy sliding mode
control with chattering elimination for nonlinear SISO systems",
Simulation Modelling Practice and Theory, Vol.17, No.7 , pp.1199-1210, 2009.

[6] J.M. Daly, D.W.L. Wang, "Output feedback sliding mode control in the presence of unknown disturbances", Systems & Control Letters Vol.58, No.3, pp.188-193, 2009.

[7] J.H. Park, S.H. Huh, S.H. Kim, S.J. Seo, G.T. Park, "direct adaptive self-structuring fuzzy controller for non affine nonlinear system", Fuzzy Sets and Systems, Vol.153, No.3, pp.429-445, 2005

[8] K.D. Sharma, A. Chatterjee, A. Rakshit, "Design of a Hybrid Stable Adaptive Fuzzy Controller Employing Lyapunov Theory and Harmony Search Algorithm", IEEE Trans. Control System Technology, Vol.18, No.6, pp.1440-1447, 2010.

[9] Li-Xin Wang, "Fuzzy systems are universal approximators", IEEE
Trans. Conference, Fuzzy Systems, pp.1163-1170, 1992.

[10] Li-Xin Wang, "Adaptive Fuzzy Systems and Control: Design
and Stability Analysis", PTR Prentice Hall, 1994.

[11] S. Li, D. Cheng, "Adaptive Fuzzy Stabilization for
a class of nonlinear time-delay systems", IEEE, proceedings
of the 7th World Congress On Intelligent Control and Automation,
pp.3368-3373, June 25-27, 2008, Chongqing, China.

[12] S. Labiod, T.M. Guerra, "Adaptive fuzzy control of a class
of SISO nonaffine nonlinear systems", Fuzzy Sets and Systems, Vol.158, No.10, pp.1126-1137, 2006.

[13] S. Tong, X. He, Y. Li, "Direct adaptive fuzzy backstepping robust
control for single input and single output uncertain nonlinear
systems using small-gain approach", Information Sciences,
Vol.180, No.9, pp.1738-1758, 2010.

[14] X. Li, D. Wang, Z. Peng, G. Sun, "Adaptive Fuzzy Control for a
Class of Non-affine Systems", IEEE, International Conference on
Intelligent Control and Information Processing, pp.561-565, August
13-15, 2010-Dalian, China.

[15] Y.S. Huang, D.S. Xiao, X.X. Chen, Q.X. Zhu, Z.W. Wang, "
tracking-based decentralized hybrid adaptive output feedback fuzzy
control for a class of large-scale nonlinear systems", Fuzzy Sets
and Systems, Vol.171, No.1, pp.72-92, 2011.

[16] Y.-J. Liu, S.-C. Tong, W. Wang, "Adaptive fuzzy output tracking
control for a class of uncertain nonlinear systems", Fuzzy Sets and
Systems, Vol.160, No.19, pp.2727-2754, 2009.

[17] Y.T. Kim, Z.Z. Bien, "Robust adaptive fuzzy control in the
presence of external disturbance and approximation error", Fuzzy
Sets and Systems, Vol.148, No.3, pp.377-393, 2004.

[18] 李祖聖，"高等模糊控制講義"，國立成功大學電機系。

[19] 黃正能，"非線性系統分析講義"，國立成功大學系統系。

[20] 楊憲東，" 控制理論及應用講義"，國立成功大學航太系。