本論文針對含有匹配與非匹配干擾之非線性系統提出一個適應順滑模態控制器的設計方法。藉由李亞普諾夫穩定性理論與線性矩陣不等式最佳化技術可得到所設計順滑面函數之係數。含有適應機制的控制器也是藉由李亞普諾夫穩定性理論來設計，因此在不需要知道匹配干擾上界的情形下，所設計的控制器不僅可使得系統軌跡在有限的時間內進入順滑面，並且在系統進入順滑模態之後可有效抑制非匹配擾動對於受控系統之影響，進而達到漸進穩定性。此外本論文所提之控制器設計方法可直接應用於一類欠致動系統。最後，分別以數值範例及實際應用來驗證控制器的可行性。

A methodology of designing an adaptive sliding mode controller for a class of nonlinear systems with matched and mismatched perturbations is proposed in this thesis. A specific designed sliding surface function is presented first, whose coefficients are determined by using Lyapunov stability theorem and linear matrix inequality (LMI) optimization technique. Without requiring the upper bounds of matched perturbations, the controller with adaptive mechanisms embedded is also designed by using Lyapunov stability theorem. The proposed control scheme not only can drive the trajectories of the controlled systems reach sliding surface in finite time, but also is able to suppress the mismatched perturbations when the controlled systems are in the sliding mode, and achieve asymptotic stability. In addition, the proposed control scheme can be directly applied to a class of underactuated systems. A numerical example and a practical experiment are given for demonstrating the feasibility of the proposed control scheme.

Abstract i
List of Figures iv
List of Tables vi
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . . . . . . 4
Chapter 2 Design of SlidingMode Controllers 5
2.1 System Descriptions and Problem Formulations . . . . . . . . . . . . . . 5
2.2 Design of Sliding Surface and Controllers . . . . . . . . . . . . . . . . . 8
2.3 Determination of the design Parameters in the Sliding Surface Function
and Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Chapter 3 Example and Application 31
3.1 Numerical example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.2 Practical Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
Chapter 4 Conclusions 56
Bibliography 57

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