利用李亞普諾夫理論(Lyapunov Theorem)，本論文提出一個半最佳參考模式調適控制器，用來穩定某些具有非線性輸入的不確定系統。本控制包括兩種主要型式。第一種型式是在假設無擾動的情況下之最佳回授控制器。第二種型式為適應控制器，具有自動調適擾動或擾動估測誤差之上界功能。本控制器將保證 uniformly ultimately boundness 的特性，並分析其中參數的特性。最後，本論文提供一個範例以驗証控制器之可行性。

By using Lyapunov stability theorem, a quasi-optimal model reference adaptive control (QOMRAC) scheme is presented in this thesis to stabilize a class of uncertain systems with input nonlinearity. This control scheme contains two main types of controllers. The first type is a linear feedback controller, which is an optimal controller if the controlled systems do not have any perturbations. The second type is an adaptive controller, which is used for adapting the unknown upper bound of perturbation or perturbation estimation error. The property of uniformly ultimately boundness is guaranteed when employing the proposed control scheme, and the effects of each design parameter on the dynamic performance are also analyzed. An example is demonstrated for showing the feasibility of the proposed control scheme.

Contents
Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . 2
Chapter 2 Quasi-Optimal Model Reference Adaptive control 4
2.1 System Descriptions and Problem Formulations . . . . . . . . . 4
2.2 Quasi-Optimal Control for a Nominal System . . . . . . . . . . 8
2.3 Design of Robust Tracking Controllers and Analysis of Stability 10
2.4 Summary of Design Procedure . . . . . . . . . . . . . . . . . . 18
Chapter 3 Quasi-Optimal Model Reference Adaptive Control with
Perturbation Estimator 19
3.1 Design of the Perturbation Estimator . . . . . . . . . . . . . . . 19
3.2 Design of Robust Tracking Controller with Perturbation Estimator 21
3.3 Summary of Design Procedure . . . . . . . . . . . . . . . . . . 30
Chapter 4 Computer Simulations 31
Chapter 5 Conclusions 72
References 73

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