本論文針對具有匹配及非匹配擾動之分數階非線性系統設計一個適應性順滑模態控制器以解決系統狀態校準問題。首先設計順滑平面，接著引入適應機制來設計控制器，使得狀態軌跡進入此順滑平面。由於適應機制及擾動估測的架構，使得擾動及擾動估測的上界資訊不需要事先預知。在此控制架構下確實能使狀態在有限時間內到達順滑平面並且停留在平衡點上。最後，本論文提供一個數值及一個實際範例來驗證其可行性。

In this thesis a design methodology of adaptive sliding mode controller was proposed for a class of multi-input fractional-order nonlinear systems with matched and mismatched perturbations to solve state regulation problems. The sliding surface is firstly introduced, and then the controller is designed with adaptive mechanisms and perturbation estimator embedded. Due to the employed adaptive and perturbation estimation mechanisms, the upper bounds of the perturbations and perturbation estimation errors do not need to be known in advance. The resultant control scheme is capable of driving the controlled states into the equilibrium point and stay thereafter within a finite time. Finally, a numerical example and a practical application are given for demonstrating the feasibility of the proposed control scheme.

論文審定書 ……………………………………………………………………… i
誌謝 …………………………………………………………………………........ ii
中文摘要 ………………………………………………………………………… iii
Abstract …………………………………………………………………………. iv
List of Figures …………………………………………………………............. vii
Chapter 1 Introduction 1
1.1 Motivation …………………………………………………………………… 1
1.2 Brief Sketch of the Contents ……………………………………………… 2
Chapter 2 Design of Adaptive Sliding Mode Controllers 4
2.1 System Descriptions and Problem Formulations …………………….… 4
2.2 Preliminaries of Fractional Calculus …………………………………...... 5
2.3 Design of Sliding Surface ……………………………………………….. 10
2.4 Design of Fractional Derivative Estimator ……………………………... 12
2.5 Design of Controllers …………………………………………………….. 15
2.6 Stability Analysis ……………………………………………………......... 18
Chapter 3 Computer Simulation and Practical Application 22
3.1 Numerical Example ……………………………………………………… 22
3.2 Practical Application …………………………………………………….. 24
Chapter 4 Conclusions 35
Bibliography 36
Appendix 45

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