基於李亞普諾夫穩定性理論，本論文提出適應區塊步階回歸控制器用來穩定具有非線性輸入之多輸入擾動系統。在設計的過程中，模糊系統主要是用來逼近動態系統中非線性函數之未知的反函數，以便於設計控制器，因此非線性輸入函數不需要滿足區間條件的限制。而步階回歸控制器則是根據受控體的區塊個數 (m 個)，設計出前 m−1 塊的虛擬控制器與第 m 層的控制輸入。在這些虛擬控制器與控制輸入中包含了適應增益，以用來估測擾動與模糊反函數估測誤差之上界常數，因此在不需要知道干擾上界的情況之下，仍能夠保證系統之狀態有漸進穩定的特性。最後，本文提出一個數值範例與實際例子來驗證本控制架構的可行性。

Based on the Lyapunov stability theorem, a design methodology of adaptive block backstepping control scheme is proposed in this thesis for a class of multi-input perturbed nonlinear systems with input nonlinearities to solve regulation problems. Fuzzy control method is utilized to estimate the unknown inverse input functions in order to facilitate the design of the proposed control scheme, so that the sector condition need not to be satisfied. According to the number of block m in the plant to be controlled, m−1 virtual input controllers are designed from the first block to the (m−1)th block. Then the proposed robust controller is designed from the last block. Adaptive mechanisms are also employed in the virtual input controllers as well as the robust controller, so that the least upper bounds of perturbations and estimation errors of inverse input functions are not required. The resultant control system is able to achieve asymptotic stability. Finally, a numerical example and a practical example are given for demonstrating the feasibility of the proposed control scheme.

Abstract i
List of Figures iv
Chapter 1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Brief Sketch of the Contents . . . . . . . . . . . . . . . . . . . . . . . 3
Chapter 2 Design of AdaptiveBackstepping Controllerswith Fuzzy Inverse
Function Estimators 4
2.1 System Descriptions and Problem Formulations . . . . . . . . . . . . . . 4
2.2 Design of Fuzzy Inverse Function Estimators . . . . . . . . . . . . . . . 7
2.3 Design of Adaptive Backstepping Controllers . . . . . . . . . . . . . . . 10
2.4 Stability Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Chapter 3 Numerical Example and Application 38
3.1 Numerical Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Practical Application . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Chapter 4 Conclusions 82
Bibliography 83
Appendix A 91
Appendix B 93
Appendix C 94
Appendix D 96

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