基於李亞諾夫之穩定定理(Lyapunov Theorem)，本論文針對含有非線性及死區之多輸入系統，提出利用適應性步階回歸技術來設計控制器以解決regulation問題。在設計的過程中，根據受控體的區塊個數(m個)，在前m-1個區塊中，每個區塊分別設計虛擬輸入控制器，然後，在第m個區塊設計強健控制器。在虛擬輸入和強健控制器中，加入適應增益來估測一些未知干擾的上界常數，這樣一來，系統擾動的上界即可不必事先知道。在穩定度分析中可得知，假設所有的控制器輸入皆在死區外，系統可達到漸近穩定之效果，若任一控制輸入在死區內，則系統能達到 uniformly ultimately bounded (UUB)之性能。最後，本論文提供一個數值範例及一個實際應用的例子以驗證本控制器的可行性。

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping controller is proposed in this thesis for a class of multi-input systems with input nonlinearity and dead zone to solve regulation problems. According to the number of block (m) in the plant to be controlled, m-1 virtual inputs are designed from the first block to the (m-1)th block. The proposed robust controller is designed from the last block. Adaptive mechanisms are also employed in each of the virtual inputs and the robust controller, hence the knowledge of the least upper bounds of perturbations is not required. Stability analysis shows that the controlled system is able to achieve asymptotic stability if all the control inputs is outside of the dead zone, and uniformly ultimately bounded is achieved if any one of the designed control inputs is in the dead zone. A numerical and a practical example are given for demonstrating the feasibility of the proposed control scheme.

論文審定書 ……………………………………………………………………… i
致謝 ……………………………………………………………………………… 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 ……………………………………………… 3
Chapter 2 Design of Adaptive Backstepping Controllers 4
2.1 System Descriptions and Problem Formulations ………………………...4
2.2 Design of Adaptive Backstepping Controllers …………………………… 7
Chapter 3 Numerical Example and Application 32
3.1 Numerical Example ………………………………………………………... 32
3.2 Practical Application ……………………………………………………… 36
Chapter 4 Conclusions 60
Bibliography 61
Appendix A 68
Appendix B 70

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