本論文基於李亞普諾夫之穩定性定理(Lyapunov Theorem)，針對具有匹配與非匹配擾動的多輸入多輸出動態系統中提出一個適應順滑模態控制器以解決系統校準的問題。為了抑制受控系統中的非匹配擾動，將調適機制應用於順滑面及控制器的設計中，使得在設計控制方法時，控制器將自動調適未知擾動上界，以致於部份擾動之上界資訊是不需要知道的。藉由此順滑面設計所得到的虛擬控制力，不僅可在系統進入順滑模態之後有效抑制非匹配擾動對受控系統之影響，進而達到漸進穩定性能之要求，而且由於控制器中導入調適機制，將使得系統狀態軌跡將在有限時間內進入順滑面。最後，本論文提供一個數值範例及實際裝置的範例以驗證所提出控制器的可行性。

Based on the Lyapunov stability theorem, an adaptive sliding mode control scheme is proposed in this thesis for a class of mismatched perturbed multi-input multi-output (MIMO) dynamic systems to solve regualtion problems. The sliding surface function is firstly designed by treating some state variables as a pseudo controllers through the usage of sliding function to stabilize the rest of state variables. In this thesis the number of these pseudo controllers is less than that of the state variables to be stabilized. The second step is to design the controllers so that the trajectories of the controlled systems are able to reach sliding surface in a finite time. Some adaptive mechanisms are embedded in the sliding surface function and sliding mode controllers, so that not only the mismatched perturbations can be suppressed during the sliding mode, but also the information of upper bounds of some perturbations are not required when designing the sliding surface function and controllers. Once the controlled system enters the sliding mode, the state trajectories can achieve asymptotical stability under certain conditions. A numerical example and a practical example are given to demonstrate the feasibility of the proposed design technique.

Abstract i
List of Figures iv
List of Notations v
Chapter 1 Introduction 1
1.1 Motivation 1
1.2 Brief Sketch of the Contents 3
Chapter 2 Design of Adaptive Sliding Mode Controllers 5
2.1 System Descriptions and Problem Formulations 5
2.2 Design of the Sliding Surface Function 9
2.3 Stability of the System in the Sliding Mode 11
2.4 Design of Adaptive Sliding Mode Controllers 18
2.5 Summary and Design Procedure 23
Chapter 3 Examples and Simulations 24
3.1 Numerical Example 24
3.2 Practical Example 27
Chapter 4 Conclusions 38
Appendix 39
References 48

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