本論文主要是探討區間式第二型模糊邏輯的設計與其應用。首先以第二型模糊邏輯為基礎，開發出新的區間式第二型模糊邏輯控制器。此第二型模糊邏輯控制器在設計過程中並不需要受控系統詳細準確的數學模式，文中詳述了設計步驟並以50%參數變化的區間式線性系統為例來說明該控制器的有效性。為了更了解該控制器的性能，我們測試了不同形狀的歸屬函數及各種不同數目的規則庫。由模擬結果得知，區間式第二型模糊邏輯控制器的表現比第一型的模糊邏輯控制器較優，而在規則庫的數目愈少時，則此特性更趨明顯。然後，滑動模式控制的概念加入先前設計的區間式第二型模糊邏輯控制器而建構出區間式第二型模糊滑動模式控制器，文中詳述了區間式第二型模糊滑動模式控制器的設計步驟。接著利用李亞普諾夫理論來驗證此模糊控制器的穩定性。為了說明控制器的有效性，將此控制器應用於倒單擺系統、度芬混沌系統、以及統一化混沌系統。模擬結果顯示出，當系統有不確定性及外在擾動存在時，區間式第二型模糊滑動模式控制器的表現優於第一型模糊滑動模式控制器，區間式第二型模糊邏輯控制器以及第一型的模糊邏輯控制器。
最後，適應控制法則導入於先前的區間式第二型模糊滑動模式控制器上，針對輪型機器人建構出智慧型控制器，整合了運動控制及區間式第二型適應模糊滑動模式動力控制。在此採用了李亞普諾夫理論來證明此智慧型控制器的穩定性。模擬結果顯示出，在輪型機器人的循跡控制上，本智慧型控制器性能表現優於傳統的適應模糊滑動模式動力控制器，而對外加擾動存在時亦有較佳的表現。

In this dissertation, we propose a novel interval type-2 fuzzy logic controller (IT2-FLC) for interval system first. The precise mathematical model of the controlled plant is not required to design this IT2-FLC. Design procedure of the IT2-FLC is explored in detail. A typical linear interval system with 50% parameter variations is adopted to demonstrate the effectiveness of the proposed IT2-FLC. For better understanding the performance of IT2-FLC, numerous shapes of membership functions and variation of rule numbers of rule table are evaluated for simulation thoroughly. The simulation results are compared with those from type-1 fuzzy logic controller (T1-FLC) under same conditions. It shows that the performance of IT2-FLC is much better than that of T1-FLC if the number of rule is reduced. Then, the proposed IT2-FLC is combined with sliding-mode control (SMC) scheme as the interval type-2 fuzzy sliding-mode control (IT2-FSMC) for linear and nonlinear systems which inherits the benefits of these two methods. The objective of the controller is to allow the system to move to the sliding surface and remain in on it so as to ensure the asymptotic stability of the closed-loop system. The Lyapunov stability method is adopted to verify the stability of the proposed controlled system. A typical second order linear interval system with 50% parameter variations and disturbances, such as an inverted pendulum with variation of pole characteristics, a Duffing forced oscillation with uncertainty and disturbance, and a unified chaotic system are adopted to illustrate the validity of the proposed method. The simulation results show that the IT2-FSMC achieves the best tracking performance in comparison with the type-1 Fuzzy logic controller (T1-FLC), the IT2-FLC, and the type-1 fuzzy sliding-mode controller (T1-FSMC).
Finally, a combined intelligent technique is proposed for controlling the trajectory-tracking of a nonholonomic wheeled mobile robot (WMR), which comprises kinematic control and an interval type-2 adaptive fuzzy sliding-mode dynamic control (IT2-AFSMDC). The kinematic model is introduced first, and then the control gains can be obtained from the back-stepping method as the input of the dynamic model. The IT2-AFSMDC is propounded for the dynamic part, a combination of the interval type-2 fuzzy logic control (IT2-FLC) and the type-1 adaptive fuzzy sliding-mode dynamic control (T1-AFSMDC), which inherits the benefits of these two methods, and adaptive law is introduced to cope with the uncertainties and disturbances of the system. The trajectory-tracking stability is proved by the Lyapunov stability analysis. Computer simulations demonstrate the validity of the proposed method. The simulation results show that the tracking performance of the IT2-AFSMDC is better than that of the T1-AFSMDC.

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